Let f : R → R, g : R → R be two functions defined by f(x) = x² + x + 1 and g(x) = 1 – x². Write fog(–2).

Question

Let f : R → R, g : R → R be two functions defined by f(x) = x 2 + x + 1 and g(x) = 1 – x 2 . Write fog(–2).

Philoid · Accepted Answer

Formula :- (I)Let f : AB and g : BC be two functions.

Then, the composition of f and g, denoted by g o f, is defined as the function g o f : AC

given by g o f (x) = g (f (x))

Given:-

(i)f : R → R

(ii)g : R → R

(iii) f(x) = x² + x + 1

(iv)g(x) = 1 – x²

Fog(-2)=f(g(-2))

Fog(-2)=f(1-(-2)²)

Fog(-2)=f(-3)

Fog(-2)=(-3)²-3+1=7

Let f : R → R, g : R → R be two functions defined by f(x) = x2 + x + 1 and g(x) = 1 – x2. Write fog(–2).