Question

Let g(x)=2x and h(x)=x^2+4 find the value. (hog)(a)

Answer 1

To find (h∘g)(a), first calculate g(a) which is 2*a, then substitute this into h(x) to get h(2a) = (2a)² + 4, and simplify to 4a² + 4.

Step-by-step explanation:

The student is asking to find the value of “(h∘g)(a)”, which means we are looking for the composition of the functions h(x) and g(x) evaluated at 'a'. Since g(x)=2x and h(x)=x²+4, we first apply the function g to 'a', resulting in 2a, and then apply the function h to this result. Thus, we need to calculate h(g(a)), which is h(2a) = (2a)² + 4.

The next step is to substitute 2a into the equation h(x) = x² + 4: (2a)² + 4 = 4a² + 4. This gives us the value of the composition of functions h(g(a)) at the point 'a'. This procedure demonstrates an understanding of function composition which is a fundamental concept in algebra and precalculus.

Answer 2

in short, (h o g)(a) is just h( g(a) ).

so what we can do is simply get g(a) first and then plug that in h(x).


`\bf \begin{cases} g(x)&=2x\\ h(x)&=x^2+4\\ (h\circ g)(a)&=h(~~g(a)~~) \end{cases} \\\\\\ g(a)=2(a)\implies g(a)=2a \\\\\\ h(~~g(a)~~)\implies h(~~2a~~)=(2a)^2+4 \\\\\\ h(~~2a~~)=(2^2a^2)+4\implies h(~~2a~~)=4a^2+4`