Question

f(x)=x2+9 and g(x)=x2-8, find the following functions. a. (f * g) (x); b. (g * f)(x)...

f(x)=x2+9 and g(x)=x2-8, find the following functions. a. (f * g) (x); b. (g * f)(x) c. (f * g)(4);

d. (g * f)(4)

Homework Answers

Answer #1

Given that

f(x) = x2+9 and

g(x) = x2-8

a. (f * g)(x)= f(x) g(x)

=  (x2+9) (x2-8)

= x2 x2 - x2 8 +9 x2 -98

= x4- 8x2+9x2 -72

= x4+x2-72

b. (g * f)(x)= g(x) f(x)

= (x2-8)  (x2+9)

= x2 x2 +x2 9 -8 x2 -89

=  x4+ 9x2-8x2 -72

= x4+x2-72.

c. Since (f * g)(x)= x4+x2-72 ................(1)

putting x=4 in above equation ,we get

(f * g)(4)= 44+42-72

= 256+16-72

=200

d. Since (g * f)(x)= x4+x2-72 ................(2)

putting x=4 in above equation ,we get

(g * f)(4)= 44+42-72

= 256+16-72

=200

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