Question

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)

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