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Question
If f (x) = 2x + 3 , g(x) = 1−2x and h(x) = 3x, then find f o (g o h).
If f (x) = 2x + 3 , g(x) = 1−2x and h(x) = 3x, then find f o (g o h).
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Solution
The correct option is C 5 − 12x
Given: f(x) = 2x + 3, g(x) = 1−2x, h(x) = 3x
Now, (f o g)(x) = f (g(x))
= f (1−2x)
= 2(1−2x)+ 3
= 5−4x
Then, (f o g) o h(x) = (f o g)(h(x))
= (f o g)(3x)
= 5−4(3x)
⇒ (f o g) o h(x) = 5−12x
Thus, (f o g) o h(x) = 5−12x
Given: f(x) = 2x + 3, g(x) = 1−2x, h(x) = 3x
Now, (f o g)(x) = f (g(x))
= f (1−2x)
= 2(1−2x)+ 3
= 5−4x
Then, (f o g) o h(x) = (f o g)(h(x))
= (f o g)(3x)
= 5−4(3x)
⇒ (f o g) o h(x) = 5−12x
Thus, (f o g) o h(x) = 5−12x
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