Back to Solve for inverse function — Problem 2 · Task Set 39

HSF.BF.B.4.a Tutor Intake — Finding and Using Inverse Functions

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·standard·hsf-bf-b-4a

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Concepts

A student wants to find $f^{-1}(x)$ for $f(x) = 5x - 3$ . Which sequence
of steps is correct?

Write $y = 5x - 3$ ; solve for $x$ to get $x = \frac{y+3}{5}$ ; write
$f^{-1}(x) = \frac{y+3}{5}$ .

Write $y = 5x - 3$ ; swap $x$ and $y$ to get $x = 5y - 3$ ; solve for $y$
to get $y = \frac{x+3}{5}$ ; write $f^{-1}(x) = \frac{x+3}{5}$ .

Write $y = 5x - 3$ ; swap $x$ and $y$ to get $x = 5y - 3$ ; solve for $y$
to get $y = \frac{x-3}{5}$ ; write $f^{-1}(x) = \frac{x-3}{5}$ .

Write $y = 5x - 3$ ; replace $x$ with $-x$ to get $y = -5x - 3$ ; write
$f^{-1}(x) = -5x - 3$ .