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I need help please with this 1 problem

I Need Help Please With This 1 Problem class=

Sagot :

Answer:

See below, please

Step-by-step explanation:

We know

[tex]f(x) = {x}^{2} + 3x - 7[/tex]

[tex]g(x) = 3x + 5[/tex]

[tex]h(x) = 2 {x}^{2} - 4[/tex]

Hence

[tex]f(g(x))[/tex]

[tex] = {(3x + 5)}^{2} + 3 \times (3x + 5) - 7[/tex]

[tex] = (9 {x}^{2} + 30x + 25) + (9x + 15) - 7[/tex]

[tex] = 9 {x}^{2} + 39x + 33[/tex]

[tex]h(g(x))[/tex]

[tex] = 2 \times {(3x + 5)}^{2} - 4[/tex]

[tex]2 \times (9 {x}^{2} + 30x + 25) - 4[/tex]

[tex] = 18 {x}^{2} + 60x + 50 - 4[/tex]

[tex] = 18 {x}^{2} + 60x + 46[/tex]

[tex](h - f)(x)[/tex]

[tex] = h(x) - f(x)[/tex]

[tex] = (2 {x}^{2} - 4) - ( {x}^{2} + 3x - 7)[/tex]

[tex] = {x}^{2} - 3x + 3[/tex]

[tex](f + g)(x)[/tex]

[tex] = f(x) + g(x)[/tex]

[tex] = ( {x}^{2} + 3x - 7) + (3x + 5)[/tex]

[tex] = {x}^{2} + 6x - 2[/tex]

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