Horizontal Line Test for Function to Have Inverse
Read this topicProblems 22
- Which of the following functions have function inverses?
- Let f:{1,2,3}→{a,b,c}f:\{1,2,3\} \to \{a,b,c\}f:{1,2,3}→{a,b,c}. Which of the following definitions of fff have a function inverse?
- Let fff be an invertible function (i.e. a function which passes the horizontal line test) and ggg be any function. In terms of fff and ggg, find a function hhh which satisfies f…
- Select all of the following graphs which are one-to-one functions
- Select all of the following graphs which are one-to-one functions.
- Which of the following functions have inverses?
- Let f(x)=axnf(x) = ax^nf(x)=axn for a∈Ra \in \mathbb{R}a∈R (real numbers) and n∈Zn \in \mathbb{Z}n∈Z (integers). Which values of nnn make fff invertible?
- True or False\text{True or False}True or False === Linear functions are always injective.
- True or False\text{True or False}True or False === A linear function of the form y=ax+by=ax+by=ax+b, where aaa and bbb are real numbers and greater than zero, is always injective.
- True or False\text{True or False}True or False === The inverse of f(x)=x+3f(x)=\sqrt x+3f(x)=x+3 IS a function.
- True or False\text{True or False}True or False === The inverse of f(x)=x2−6x+9f(x)=x^2-6x+9f(x)=x2−6x+9 IS a function.
- Let f(x)=xaf(x)=x^af(x)=xa where aaa is a nonzero real number. What values of aaa produce an inverse that is a function?
- True or False\text{True or False}True or False === The inverse of f(x)=ln(x)f(x)=\ln(x)f(x)=ln(x) is also a function.
- Does the function f(x)=3x+8x−2f(x)=\dfrac{3x+8}{x-2}f(x)=x−23x+8 have an inverse?
- Does the function f(x)=x3−9xf(x)=x^3-9xf(x)=x3−9x have an inverse?
- Does the function f(x)=x3−9x2+27x−27f(x)=x^3-9x^2+27x-27f(x)=x3−9x2+27x−27 have an inverse?
- Does the function f(x)=x+25−3f(x)=\sqrt[5]{x+2}-3f(x)=5x+2−3 have an inverse?
- Does the function f(x)=xxf(x)=x^xf(x)=xx have an inverse?
- Does the graph above pass the horizontal line test on the interval (-3,0]?
- True or False\text{True or False}True or False === The inverse of f(x)=x2, x≥0f(x)=x^{2},\; x\geq0f(x)=x2,x≥0 is also a function.
- True or False\text{True or False}True or False === The inverse of f(x)=x3f(x)=x^{3}f(x)=x3 is also a function.
- True or False\text{True or False}True or False === The inverse of f(x)=1x, x≠0f(x)=\frac{1}{x},\; x\neq0f(x)=x1,x=0 is also a function.