Question

I need help please with this 1 problem

Answer 1

Answer:

See below, please

Step-by-step explanation:

We know

$f(x) = {x}^{2} + 3x - 7$

$g(x) = 3x + 5$

$h(x) = 2 {x}^{2} - 4$

Hence

$f(g(x))$

$= {(3x + 5)}^{2} + 3 \times (3x + 5) - 7$

$= (9 {x}^{2} + 30x + 25) + (9x + 15) - 7$

$= 9 {x}^{2} + 39x + 33$

$h(g(x))$

$= 2 \times {(3x + 5)}^{2} - 4$

$2 \times (9 {x}^{2} + 30x + 25) - 4$

$= 18 {x}^{2} + 60x + 50 - 4$

$= 18 {x}^{2} + 60x + 46$

$(h - f)(x)$

$= h(x) - f(x)$

$= (2 {x}^{2} - 4) - ( {x}^{2} + 3x - 7)$

$= {x}^{2} - 3x + 3$

$(f + g)(x)$

$= f(x) + g(x)$

$= ( {x}^{2} + 3x - 7) + (3x + 5)$

$= {x}^{2} + 6x - 2$