×

## Functions

Functions map an input to an output. For example, the function f(x) = 2x takes an input, x, and multiplies it by two. An input of x = 2 gives you an output of 4. Learn all about functions.

# Inverse Functions

Consider 3 functions $$f(x), g(x),$$ and $$h(x)$$ above.

Which has an inverse function ?

Let $$f(x)=2x-7,$$ and let $$g(x)=f^{-1}(x)$$. What is the value of $$g(15)+g^{-1}(17)$$?

 Details and assumptions

• $$g^{-1}(x)$$ denotes the inverse function of $$g(x)$$.

If $$f^{-1}(2)=0$$ and $$(f \circ f)(0) = 20$$ for $$f(x)=ax+b$$, what is $$a+b$$?

Consider the function $$f(x) =$$ $$\begin{cases} 2x & (x \ge 1) \\ 2(1-k)x + 2k & (x < 1). \end{cases}$$

If $$f^{-1}(x)$$ exists, find the value of the constant $$k.$$

 Details and assumptions

• $$f^{-1}(x)$$ denotes the inverse function of $$f(x).$$

Consider a function $$f: X \to Y,$$ where $$X = \{x |\, 0 \le x \le 1\}$$ and $$Y = \{y|\, a \le y \le b\}.$$

If $$f(x) = 3x + 2,$$ and $$f^{-1}(x)$$ exists, find the values of $$a , b.$$

 Details and assumptions

• $$f^{-1}(x)$$ denotes the inverse function of $$f(x).$$
×