When 𝑓(𝑥) = 3𝑥 − 5 and 𝑔(𝑥) = 2𝑥2 − 5 , find 𝑓(𝑔(𝑥))

Question

When 𝑓(𝑥) = 3𝑥 − 5 and 𝑔(𝑥) = 2𝑥2 − 5 , find 𝑓(𝑔(𝑥))

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Solution

To find the composition of the functions 𝑓(𝑔(𝑥)), we substitute 𝑔(𝑥) into 𝑓(𝑥).

Step 1: Write down the function 𝑓(𝑥) = 3𝑥 − 5

Step 2: Substitute 𝑔(𝑥) = 2𝑥² - 5 into 𝑓(𝑥). Wherever there is an 𝑥 in the function 𝑓, replace it with 𝑔(𝑥).

So, 𝑓(𝑔(𝑥)) = 3(𝑔(𝑥)) - 5 = 3(2𝑥² - 5) - 5

Step 3: Simplify the expression.

𝑓(𝑔(𝑥)) = 6𝑥² - 15 - 5 = 6𝑥² - 20

So, 𝑓(𝑔(𝑥)) = 6𝑥² - 20.

This problem has been solved

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