Questions: Given that h(x)=7x-4, x ≥ 0; 4x+3, x<0. Find h(-2)

Transcript text: Given that $h(x)=\left\{\begin{array}{l}7 x-4, x \geq 0 \\ 4 x+3, x<0\end{array}\right.$ Find $h(-2)$

Solution

Solution Steps

To find $ h(-2) $, we need to determine which piece of the piecewise function applies. Since $-2 < 0$, we use the second piece of the function, $ h(x) = 4x + 3 $. Substitute $-2$ into this expression to find the value of $ h(-2) $.

Step 1: Determine the Applicable Piece of the Function

The function $ h(x) $ is defined as a piecewise function: \[ h(x) = \begin{cases} 7x - 4, & x \geq 0 \\ 4x + 3, & x < 0 \end{cases} \] Since we need to find $ h(-2) $ and $-2 < 0$, we use the second piece of the function: $ h(x) = 4x + 3 $.

Step 2: Substitute the Value into the Function

Substitute $ x = -2 $ into the expression $ 4x + 3 $: \[ h(-2) = 4(-2) + 3 \]

Step 3: Simplify the Expression

Calculate the expression: \[ h(-2) = -8 + 3 = -5 \]