If the function f ( x ) = { x + 1 2 x + 1 i f x ≤ 1 i f 1

Question

If the function f ( x ) = { x + 1 2 x + 1 ​ i f x ≤ 1 i f 1 < x ≤ 2 ​ and g ( x ) = { x 2 x + 2 ​ − 1 ≤ x ≤ 2 2 ≤ x ≤ 3 ​ , then the number of roots of the equation f ( g ( x )) = 2 is

TestHub · Accepted Answer

f ( g ( x )) = { x 2 + 1 2 x 2 + 1 ​ − 1 ≤ x ≤ 1 1 < x ≤ 2 ​ ​ We have: f ( g ( x )) = 2 ⇒ { x 2 + 1 = 2 2 x 2 + 1 = 2 ​ ⇒ x = ± 1 ⇒ x = ± 2 ​ 1 ​ ​ The number of solutions is 2 .

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