HSF.BF.B.4.a: Solve for inverse function — Practice

Warm-Up: Review What You Know

These problems review skills you have already learned.

If $f$ and $g$ are inverse functions, which of the following must be true?

$f(g(x)) = 0$

$f(g(x)) = x$

$f(g(x)) = f(x)$

$g(x) = -f(x)$

Solve the equation $3x - 7 = 11$ for $x$ .

For $f(x) = 2x + 5$ , what is the value of $x$ when $f(x) = 13$ ?

Find the inverse of each function. Show your steps.

Find $f^{-1}(x)$ for $f(x) = 4x - 3$ .

Express your answer in the form $f^{-1}(x) = \frac{x + a}{b}$ .
Enter just the value of $a$ (the number added in the numerator).

Find $f^{-1}(x)$ for $f(x) = \dfrac{x - 5}{2}$ .

Enter the coefficient of $x$ in the expression for $f^{-1}(x)$ .
(For example, if $f^{-1}(x) = 2x + 5$ , enter 2.)

$Four-step flowchart of the swap-and-solve procedure applied to f(x) = 2x³, showing each algebraic transformation$

Find $f^{-1}(x)$ for $f(x) = 2x^3$ .

Enter the denominator of the expression under the cube root in $f^{-1}(x)$ .
(For example, if $f^{-1}(x) = \sqrt[3]{\frac{x}{k}}$ , enter $k$ .)

Let $f(x) = x^2$ with domain $x \geq 0$ .
Which of the following is $f^{-1}(x)$ ?

$f^{-1}(x) = x^2$

$f^{-1}(x) = \pm\sqrt{x}$

$f^{-1}(x) = \sqrt{x}$ , for $x \geq 0$

$f^{-1}(x) = -\sqrt{x}$

Find $f^{-1}(x)$ for $f(x) = \dfrac{x + 3}{x - 2}$ , where $x \neq 2$ .

After applying the swap-and-solve method, the inverse is of the form
$f^{-1}(x) = \dfrac{ax + b}{x - c}$ .
Enter the value of $c$ .