Question

Find (h-g)(x) , (f-h)(x) , g(f(5))

Use the functions f(x)=4x+1 , g(x)=2x^2-6x , and h(x)= -x^2+3x-19
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Answer 1

• (h-g)(x) = -3x² + 9x - 19

• (f-h)(x) = x² + x + 20

• g(f(5)) = 756

Explanation:

f(x) = 4x+1

g(x) = 2x²-6x

h(x) = -x² + 3x - 19

a)

(h-g)(x) = h(x) - g(x)

= -x² + 3x - 19 - (2x²-6x)

= -x² + 3x - 19 - 2x² + 6x

combining like terms: -x² - 2x² = -3x², 3x+6x = 9x

= -3x² + 9x - 19

Therefore,

(h-g)(x) = -3x² + 9x - 19

b)

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

= 4x+1 - (-x² + 3x - 19)

= 4x+1 + x² - 3x + 19

combining like terms: 4x- 3x = x, 1+19 = 20

= x² + x + 20

Therefore,

(f-h)(x) = x² + x + 20

c)

g(f(5)) = ?

First determine f(5) by substituting x = 5 in the function f(x)

f(x)=4x+1

f(5) = 4(5) + 1

f(5) = 20+1

f(5) = 21

so

g(f(5)) = g(21)

now

substituting x = 21 in the function g(x)

g(x) = 2x²-6x

g(21) = 2(21)² - 6(21)

g(21) = 882 - 126

g(21) = 756

Therefore,

g(f(5)) = 756