Composing Functions at a Point
Read this topicExplanations 5
- (Videos) Function Operations and Composition by mathman1024 Here's a video by mathman1024 explaining how to deal with adding, subtracting, multiplying, and dividing functions. T…
By Alex Federspiel, Joshua Siktar, Anusha Rahman
- (Video) Function Operations and Composition by mathman1024 In this video by mathman1024 he goes over evaluating composite functions. Composite functions are denoted with a ∘\cir…
By Alex Federspiel, Joshua Siktar, Anusha Rahman
- There are a few different scenarios in which you might have to evaluate a composite function at a given point: using a table, using a graph, or using the expressions of the func…
By Caroline K, Jasper Brown, Alex Federspiel
- A function fff is such that if you input a number x,x,x, you spit out a number yyy by applying fff to it; that is, y=f(x).y = f(x).y=f(x). But what if you want to plug yyy into …
By Joshua Siktar, Anusha Rahman
- Function Composition Function composition is when you take two functions and combine them to make a new one. If you're given two functions, f(x)f(x)f(x) and g(x)g(x)g(x), the co…
By Anusha Rahman
Problems 43
- If f(x/2)=x+1f(x/2) = x+1f(x/2)=x+1 for all xxx, find the value of zzz that satisfies f(2z)=9f(2z)=9f(2z)=9.
- Let f(x)=5x+3f(x) = 5x + 3f(x)=5x+3 and g(x)=2x−4g(x) = 2x - 4g(x)=2x−4. What is f(g(2))f(g(2))f(g(2))? Note: This is also written as (f∘g)(2)(f \circ g)(2)(f∘g)(2).
- Let f(x)=x2−3xf(x) = x^2 - 3xf(x)=x2−3x and g(x)=8xg(x) = \frac{8}{x}g(x)=x8. What is f(g(2))f(g(2))f(g(2))? Note: This is also written as (f∘g)(2)(f \circ g)(2)(f∘g)(2).
- Let f(x)=2xf(x) = 2^xf(x)=2x and g(x)=14x2g(x) = \frac{1}{4}x^2g(x)=41x2. What is f(g(4))−f(g(2))f(g(4)) - f(g(2))f(g(4))−f(g(2))?
- In a department store you see a sign that says 50%50\%50% off clearance merchandise, so final cost CCC depends on the clearance price, ppp, according to the function C(p)C(p)C(p…
- Using the tables above, evaluate f(g(1))f(g(1))f(g(1)) and g(f(3))g(f(3))g(f(3)).
- In the graph above, g(x)=(x−3)2−1g(x) = (x-3)^2-1g(x)=(x−3)2−1 is shown in red and f(x)=−(x−3)2+6f(x)=-(x-3)^2+6f(x)=−(x−3)2+6 is shown in blue. Evaluate g(f(2)).g(f(2)).g(f(2)).
- Given f(t)=t2−tf(t)=t^2-tf(t)=t2−t and h(x)=3x+2h(x)=3x+2h(x)=3x+2, evaluate h(f(−2))h(f(-2))h(f(−2)).
- Calculate f(g(0))f(g(0))f(g(0)) and g(f(0))g(f(0))g(f(0)) if f(x)=4x+7f(x)=4x+7f(x)=4x+7 and g(x)=4−2x2.g(x)=4-2x^2.g(x)=4−2x2.
- Calculate f(g(0))f(g(0))f(g(0)) and g(f(0))g(f(0))g(f(0)) if f(x)=x+4f(x)=\sqrt{x+4}f(x)=x+4 and g(x)=12−x3.g(x)=12-x^3.g(x)=12−x3.
- If f(x)=4x+8f(x)=4x+8f(x)=4x+8 and g(x)=7−x2,g(x)=7-x^2,g(x)=7−x2, calculate f(g(0))f(g(0))f(g(0)) and g(f(0)).g(f(0)).g(f(0)).
- Calculate f(g(0))f(g(0))f(g(0)) and g(f(0))g(f(0))g(f(0)) if f(x)=1x+2f(x)=\dfrac{1}{x+2}f(x)=x+21 and g(x)=4x+3.g(x)=4x+3.g(x)=4x+3.
- Use the table above to evaluate f(g(8)).f(g(8)).f(g(8)).
- Use the table above to evaluate f(g(5)).f(g(5)).f(g(5)).
- Use the table above to evaluate g(f(5)).g(f(5)).g(f(5)).
- Use the table above to evaluate g(f(3)).g(f(3)).g(f(3)).
- Use the table above to evaluate f(f(4)).f(f(4)).f(f(4)).
- Use the table above to evaluate g(g(6)).g(g(6)).g(g(6)).
- In the graph above, g(x)=3g(x) = 3g(x)=3 is shown in red and f(x)=(x−4)2f(x)=(x-4)^2f(x)=(x−4)2 is shown in blue. Evaluate f(g(3)).f(g(3)).f(g(3)).
- In the graph above, f(x)=−x+5f(x)=-x+5f(x)=−x+5 is shown in blue and g(x)=(x−1)2+3g(x)=(x-1)^2+3g(x)=(x−1)2+3 is shown in red. Evaluate f(g(1))f(g(1))f(g(1)).
- In the graph above, f(x)=−x+5f(x)=-x+5f(x)=−x+5 is shown in blue and g(x)=(x−1)2+3g(x)=(x-1)^2+3g(x)=(x−1)2+3 is shown in red. Evaluate g(f(1))g(f(1))g(f(1)).
- In the graph above, f(x)=−x3+4f(x)=-x^3+4f(x)=−x3+4 is shown in blue and g(x)=−∣x−4∣+5g(x)=-|x-4|+5g(x)=−∣x−4∣+5 is shown in red. Evaluate g(f(0)).g(f(0)).g(f(0)).
- Above is the graph of f(x)=13(x−3)2−6.f(x)=\frac{1}{3}(x-3)^2-6.f(x)=31(x−3)2−6. Evaluate f(f(6))f(f(6))f(f(6)).
- Above is a graph of f(x)=−x+4.f(x)=-x+4.f(x)=−x+4. Use this graph to evaluate f(f(4)).f(f(4)).f(f(4)).
- In the graph above, g(x)=x4+3x3+x2+x.g(x)=x^4+3x^3+x^2+x.g(x)=x4+3x3+x2+x. Evaluate g(g(−1))g(g(-1))g(g(−1)).
- Above is the graph of g(x)=12∣x−6∣+1.g(x)=\frac{1}{2}|x-6|+1.g(x)=21∣x−6∣+1. Evaluate g(g(0))g(g(0))g(g(0)).
- Let f(x)=lnx.f(x)=\ln x.f(x)=lnx. Find f(f(1)).f(f(1)).f(f(1)).
- Suppose that f(x)=x+6.f(x)=x+6.f(x)=x+6. Find f(f(3)).f(f(3)).f(f(3)).
- Let f(x)=4x.f(x)=4^x.f(x)=4x. Evaluate f(f(12)).f\left(f\left(\frac{1}{2}\right)\right).f(f(21)).
- Let f(x)=eex.f(x) = e^{e^x}.f(x)=eex. Evaluate f(f(1))+f(1).f(f(1))+f(1).f(f(1))+f(1).
- Let f(x)=8x.f(x)=8^x.f(x)=8x. Evaluate f(f(13)).f(f(\frac{1}{3})).f(f(31)).
- Let f(x)=4xf(x)=4xf(x)=4x and g(x)=ex.g(x)=e^x.g(x)=ex. Evaluate g(f(2))⋅f(g(2)).g(f(2)) \cdot f(g(2)).g(f(2))⋅f(g(2)).
- Let f(x)=7+8xf(x) = 7+8^xf(x)=7+8x and g(x)=x2.g(x)=x^2.g(x)=x2. Evaluate g(f(13)).g(f(\frac{1}{3})).g(f(31)).
- Let f(x)=1x+3f(x)=\dfrac{1}{x+3}f(x)=x+31 and g(x)=12x2.g(x)= \dfrac{1}{2x^2}.g(x)=2x21. Evaluate f(g(3))+g(f(3)).f(g(3))+g(f(3)).f(g(3))+g(f(3)).
- Let f(x)=x3+x2+x+1f(x)=x^3+x^2+x+1f(x)=x3+x2+x+1 and g(x)=x2.g(x)=x^2.g(x)=x2. Evaluate f(g(2)).f(g(2)).f(g(2)).
- Let f(x)=x+5f(x)=x+5f(x)=x+5 and g(x)=2x2+x+7.g(x)=2x^2+x+7.g(x)=2x2+x+7. Evaluate g(f(4)).g(f(4)).g(f(4)).
- Let f(x)=xx−27f(x)=\dfrac{x}{x-27}f(x)=x−27x and g(x)=3x23.g(x)=3x^{\frac{2}{3}}.g(x)=3x32. Evaluate f(g(27))+g(f(18)).f(g(27))+g(f(18)).f(g(27))+g(f(18)).
- Let f(x)=x+1f(x)= x+1f(x)=x+1 and g(x)=x+2cos(x).g(x)=x+2\cos (x).g(x)=x+2cos(x). Evaluate f(g(0)).f(g(0)).f(g(0)).
- Let f(x)=30xf(x)=30xf(x)=30x and g(x)=x14.g(x)=x^{\frac{1}{4}}.g(x)=x41. Evaluate f(g(1))−f(g(16)).f(g(1))-f(g(16)).f(g(1))−f(g(16)).
- Let f(x)=sin(x).f(x)=\sin(x).f(x)=sin(x). Evaluate f(f(f(f(0)))).f(f(f(f(0)))).f(f(f(f(0)))).
- Let f(x)=2x+2+3.f(x)= 2^{x+2}+3.f(x)=2x+2+3. Evaluate f(f(3)).f(f(3)).f(f(3)).
- Let f(x)=x+1,f(x)= x+1,f(x)=x+1, g(x)=x+5,g(x)=x+5,g(x)=x+5, and h(x)=x2.h(x)=x^2.h(x)=x2. Evaluate f(g(h(5))).f(g(h(5))).f(g(h(5))).
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