Questions: Question Given (f(t)=t^2-t) and (h(x)=3 x+2), evaluate (h(f(2))) :

Transcript text: Question Given $f(t)=t^{2}-t$ and $h(x)=3 x+2$, evaluate $h(f(2))$ : Provide your answer below:

Solution

Solution Steps

To solve for $ h(f(2)) $, we first need to evaluate $ f(2) $ by substituting $ t = 2 $ into the function $ f(t) = t^2 - t $. Once we have the result of $ f(2) $, we substitute this value into the function $ h(x) = 3x + 2 $ to find $ h(f(2)) $.

Step 1: Evaluate $ f(2) $

We start by substituting $ t = 2 $ into the function $ f(t) = t^2 - t $: \[ f(2) = 2^2 - 2 = 4 - 2 = 2 \]

Step 2: Evaluate $ h(f(2)) $

Next, we substitute the result from Step 1 into the function $ h(x) = 3x + 2 $: \[ h(f(2)) = h(2) = 3(2) + 2 = 6 + 2 = 8 \]

Final Answer

The final result is $ \boxed{8} $.

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