Question

If f(x) = 5x + 4 and (gof)(x) = 15x + 10, find g(x).

Answer 1

To find g(x), we need to determine the function g that satisfies the composition (gof)(x) = 15x + 10, where f(x) = 5x + 4.

We can find g(x) by substituting the expression for f(x) into (gof)(x) and solving for g(x):

(gof)(x) = g(f(x))

Substituting f(x) = 5x + 4:

g(5x + 4) = 15x + 10

Now, let's simplify the equation:

g(5x + 4) = 15x + 10
g(x) = (15x + 10) / (5x + 4)

Therefore, g(x) is equal to (15x + 10) / (5x + 4).

Answer 2

(i) f(x)=∣x∣ and g(x)=∣5x−2∣

∴(gof)(x)=g(f(x))=g(∣x∣)=∣5∣x∣−2∣

And (fog)(x)=f(g(x))=f(∣5x−2∣)=∣∣5x−2∣∣=∣5x−2∣

(ii)f(x)=8x

3and g(x)=x 31

∴(gof)(x)=g(f(x))=g(8x 3 )=(8x 31 )

=2x

And (fog)(x)=f(g(x))=f(x 31 )=8(x 31 ) 3 =8x