Question

F:R-R is given by f (x) = 2x^2 +3x + 5 and the map g:R-R is given by g (x)= 4x-5 find (fog) 1 and (gof) 2

Answer 1

SOLUTION

GIVEN

• f : R → R given by f(x) = 2x² + 3x + 5

• g : R → R given by g(x) = 4x - 5

TO DETERMINE

The value of (fog)(1) and (gof)(2)

EVALUATION

Here it is given that

f : R → R given by f(x) = 2x² + 3x + 5

g : R → R given by g(x) = 4x - 5

We have

(fog)(1)

= f(g(1))

Now g(1) = 4 - 5 = - 1

Thus we get

(fog)(1)

= f(g(1))

= f( - 1 )

= 2 × (-1)² + 3 × (-1) + 5

= 2 - 3 + 5

= 4

Again

(gof)(2)

= g(f(2))

Now

f(2)

= 2 × (2)² + 3 × (2) + 5

= 8 + 6 + 5

= 19

Thus we get

(gof)(2)

= g(f(2))

= g(19)

= ( 4 × 19 ) - 5

= 76 - 5

= 71

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