Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 7 \text { and } g ( x ) = x + 2$
A) $t ^ { 2 } + t - 9$
B) $t ^ { 2 } - t - 9$
C) $t ^ { 2 } + 3 t - 9$
D) $t ^ { 2 } + t - 5$
E) $t ^ { 2 } + 3 t - 5$

Question

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 7 \text { and } g ( x ) = x + 2$ 
A) $t ^ { 2 } + t - 9$
B) $t ^ { 2 } - t - 9$
C) $t ^ { 2 } + 3 t - 9$
D) $t ^ { 2 } + t - 5$
E) $t ^ { 2 } + 3 t - 5$

Quizplus · Accepted Answer

The indicated function to evaluate is $f(g(t))$. Substituting $g(t) = t + 2$ into $f(x) = x^2 - 7$, we get $f(g(t)) = (t + 2)^2 - 7 = t^2 + 4t + 4 - 7 = t^2 + 4t - 3$. However, none of the options match this result, indicating a mistake in my initial response. Correcting this, the correct approach is to evaluate $f(g(t))$ or $g(f(t))$ based on the options provided, which seem to suggest a composition of functions not explicitly stated in the question. Given the options and the functions, the correct evaluation aligns with option A when correctly calculating $f(g(t)) = (t + 2)^2 - 7 = t^2 + 4t + 4 - 7 = t^2 + 4t - 3$, but this was a misinterpretation. The correct approach involves identifying the proper composition based on the options, which I initially failed to match correctly due to an oversight in calculation or interpretation of the function compositions.

Evaluate the Indicated Function For f(x)=x2−7 and g(x)=x+2f ( x ) = x ^ { 2 } - 7 \text { and } g ( x ) = x + 2f(x)=x2−7 and g(x)=x+2

Evaluate the Indicated Function For $f ( x ) = x ^ { 2 } - 7 \text { and } g ( x ) = x + 2$