Question

solve for input of function given output
question
given ( g(x) = -2x + 1 ), solve for ( x ) when ( g(x) = 5 ).

Explanation:

Step1: Substitute \( g(x) \) with 5

We know \( g(x) = -2x + 1 \) and \( g(x) = 5 \), so we substitute to get \( 5 = -2x + 1 \).

Step2: Subtract 1 from both sides

Subtract 1 from each side: \( 5 - 1 = -2x + 1 - 1 \), which simplifies to \( 4 = -2x \).

Step3: Divide by -2

Divide both sides by -2: \( \frac{4}{-2} = \frac{-2x}{-2} \), so \( x = -2 \).

Answer:

\( x = -2 \)