Question

I need help on these functions questions

Answer 1

Answer:

see explanation

Step-by-step explanation:

(a)

Substitute x = - 1 into f(x)

f(- 1) = 6 - 2(- 1) = 6 + 2 = 8

(b)

Substitute x = $\frac{1}{3}$ into g(x)

g($\frac{1}{3}$ ) = $\frac{9}{\frac{1}{3} }$ = 9 × 3 = 27

(c)

Substitute x = f(x) into h(x)

h(6 - 2x)

= 6 + (6 - 2x)² ← expand using FOIL

= 6 + 36 - 24x + 4x² ← collect like terms

= 4x² - 24x + 42

(d)

Substitute x = f(x) into g(x)

g(6 - 2x)

= $\frac{9}{6-2x}$

(e)

Evaluate g(12) then substitute value obtained into f(x)

g(12) = $\frac{9}{12}$ = $\frac{3}{4}$ , then

f($\frac{3}{4}$ ) = 6 - (2 × $\frac{3}{4}$ ) = 6 - $\frac{3}{2}$ = $\frac{9}{2}$

(f)

Evaluate f(- 9) then substitute the value obtained into h(x)

f(- 9) = 6 - 2(- 9) = 6 + 18 = 24 , then

h(24) = 6 + 24² = 6 + 576 = 582