Question

If f and g are real valued functions defined by f(x) = 2x - 1 and g(x) = x² then find
i. (3f - 2g) (x)
ii. (fg) (x)
iii. (√f/g) (x)
iv. (f + g + 2) (x)

Answer 1

Hi,

Given that

 f(x) = 2x - 1     and    g(x) = x²  ,     so we have

i. (3f - 2g) (x)

(3f - 2g) (x) = 3 f(x) - 2 g(x)

(3f - 2g) (x) = 3 (2x-1) - 2x²

(3f - 2g) (x) = 6x - 3 - 2x²

(3f - 2g) (x) =  - 2x² + 6x - 3

ii. (fg) (x)

(fg) (x) = (2x-1) ( x² )

(fg) (x) = f(x) . g(x)

(fg) (x) = $2x^{3} - x^{2}$

iii. (√f/g) (x)

(√f/g) (x) = $\sqrt{\frac{2x - 1}{x^{2} } }$

iv. (f + g + 2) (x)

(f + g + 2) (x) = f(x) + g(x) + 2

(f + g + 2) (x) = 2x - 1 + x² + 2

(f + g + 2) (x) = x² + 2x +1