Question

Let h(x)=2x+5h(x)=2x+5h, left parenthesis, x, right parenthesis, equals, 2, x, plus, 5 and g(x)=8-3xg(x)=8−3xg, left parenthesis, x, right parenthesis, equals, 8, minus, 3, x. What is the value of h(g(1.5))h(g(1.5))h, left parenthesis, g, left parenthesis, 1, point, 5, right parenthesis, right parenthesis?

Answer 1

The given functions were

$h(x)=2x+5\: and\:g(x)=8-3x$

Before we can evaluate $h(g(1.5))$ we need to find an expression for  $h(g(x))$.

This is the composition of the two functions. $h(g(x))$ means $g(x)$ becomes an input for $h(x)$. This means that;

$h(g(x))=h(8-3x)$

So we need to substitute, $8-3x$ wherever we see $x$ in $h(x)$

$\Rightarrow h(g(x))=2(8-3x)+5$

We expand the bracket to obtain;

$h(g(x))=2\times8-2\times3x+5$

Simplify to obtain;

$h(g(x))=16-6x+5$

$h(g(x))=21-6x$

Now we substittute $x=1.5$ in to $h(g(x))=21-6x$ to obtain,

$\Rightarrow h(g(1.5))=21-6(1.5)$

$\Rightarrow h(g(1.5))=21-9$

$\Rightarrow h(g(1.5))=12$

Hence, the value of $h(g(1.5))$ is $1.5$.

Answer 2

8x equal 5 - six because is a parenthesis