Solve the problem.
-Given $f ( x ) = | x | - 3 ; x \geq 0$, write an equation for $f ^ { - 1 } ( x )$. (Hint: Sketch $f ( x )$ and note the domain and range.)
A) $f ^ { - 1 } ( x ) = x + 3 ; x \geq - 3$
B) $f ^ { - 1 } ( x ) = | x | + 3 ; x \geq - 3$
C) $f ^ { - 1 } ( x ) = | x + 3 | ; x \geq 0$
D) $f ^ { - 1 } ( x ) = | x | + 3 ; x \geq 0$

Question

Quizplus · Accepted Answer

To find $f^{-1}(x)$, swap $x$ and $y$ in the original equation and solve for $y$. Starting with $y = |x| - 3$, swapping gives $x = |y| - 3$. Solving for $y$ gives $y = x + 3$, valid for $x \geq -3$ because the original function's range starts at $-3$.

Solve the Problem f(x)=∣x∣−3;x≥0f ( x ) = | x | - 3 ; x \geq 0f(x)=∣x∣−3;x≥0

Solve the Problem $f ( x ) = | x | - 3 ; x \geq 0$