Question

MATHEMATICS
1
If f(x) = 2x + 3,g(x) = 1 - x
${?}^{2}$
then the values of x that satisfy the equation gof(x) = 0 are
(a) 2, 2 (b) 1, -2 (c) 0,3 (d) -1,-2​

Answer 1

GIVEN :–

• f(x) = 2x + 3

• g(x) = 1 - x²

TO FIND :–

• If gof(x) = 0 then x = ?

SOLUTION :–

$\\ \implies \bf gof(x) =0$

• We should write this as –

$\\ \implies \bf g(f(x)) =0$

$\\ \implies \bf g(2x + 3) =0 \: \: \: \: \: \: \: \: \left[ \: \because \: f(x) = 2x + 3 \right]$

$\\ \implies \bf 1 - (2x + 3)^2 =0$

$\\ \implies \bf 1 = (2x + 3)^2$

$\\ \implies \bf 1 =4 {x}^{2} + 9 + 12x$

$\\ \implies \bf 4 {x}^{2} + 12x + 8 = 0$

$\\ \implies \bf {x}^{2} + 3x + 2 = 0$

$\\ \implies \bf {x}^{2} + 2x + x + 2 = 0$

$\\ \implies \bf x(x + 2) + 1(x + 2) = 0$

$\\ \implies \bf (x + 1)(x + 2)= 0$

$\\ \implies \bf x = - 1, - 2$

▪︎ Hence , Option (d) is correct.