Let f(x)=1/2x^5/2 and g(x)=2x^2. Find (f*g)(x) and (f/g)(x). Then evaluate (f*g)(9) and (f/g)(9)

Question

Let f(x)=1/2x^5/2 and g(x)=2x^2.

Find (f*g)(x) and (f/g)(x).

Then evaluate (f*g)(9) and (f/g)(9)

Please help me!

Answer 1

For (f×g)(x) the solution is as follows

(1/2)x^5/2 × 2x²

1/2 × 2 × x^5/2× x²

2/2 × x^{5/2 + 2}

1 × x^(5+4)/2

1x^9/2 .

For (f/g)(x)

((1/2)x^5/2)/2x²

(1/2)/2 × (x^5/2)/x²

(1/2) × (1/2) × x^{(5/2) - 2}

(1×1/2×2) × x^(5-4)/2

(1/4) × x^1/2.

For(f×g)(9)

Substitue x = 9 for the answer one

We get

1 × (9)^9/2

(√9)⁹

(3)⁹

^19,683

For (f/g)(9) we substitue x in answer two with 9

(1/4) × √9

(1/4) × 3

3/4