If f : R → R and g :
Question:

If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g(f(x)) = 8 are

(a) 1, 2

(b) −1, 2

(c) −1, −2

(d) 1, −2

Solution:

(c) −1, −2

f(x) = 2x + 3 and g(x) = x2 + 7

$g(f(x))=8$

$\Rightarrow(f(x))^{2}+7=8$

 

$\Rightarrow(2 x+3)^{2}+7=8$

$\Rightarrow x^{2}+3 x+2=0$

 

$\Rightarrow(x+2)(x+1)=0$

$\Rightarrow x=1 \mid=1,-2$

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