Question

If f(x) = 2x+1, g(x) = x2 then (f+g)/(fg) (x) =

Answer 1

Answer is in the pic.

Answer 2

Given :-

• f(x) = 2x + 1
• g(x) = x²

To Find :-

• (f+g)/(fg) (x)

Solution :-

Solving Numerator First :-

→ f(x) = 2x + 1

→ g(x) = x²

So ,

→ (f + g)(x) = f(x) + g(x)

→ (f + g)(x) = (2x + 1) + x²

→ (f + g)(x) = (x² + 2x + 1)

→ (f + g)(x) = (x² + x + x + 1)

→ (f + g)(x) = {x(x + 1) + 1(x+1)}

→ (f + g)(x) = {(x+1)(x+1)}

→ (f + g)(x) = (x + 1)²

Similarly,

Solving Denominator Now,

→ f(x) = 2x + 1

→ g(x) = x²

So ,

→ (f*g)(x) = f(x) * g(x)

→ (f*g)(x) = (2x +1)(x²)

→ (f*g)(x) = (2x³ + x²)

Therefore,

→ {(f+g)/(fg)} (x) = (x + 1)² / (2x³ + x²) (Ans.)