If f(x) = x² + 1 and g(x) = x - 4, which value is equivalent to f(g(10))?

Solution:

It is given that,

f(x) = x² + 1

g(x) = x - 4

We know that f(g(x) is a composite function, that takes all the outputs of g(x) as its inputs.

f(g(x)) = f(x - 4)

But f(x) = x² + 1

f(g(x)) = (x - 4)² + 1

We know that, (a - b)² = a² - 2ab + b²

f(g(x)) = x² - 8x + 16 +1

f(g(x)) = x² - 8x + 17.

Then,

f(g(10)) = 10² - 8(10) + 17

f(g(10)) = 100 - 80 +17

f(g(10)) = 37

Therefore, the value equivalent to f(g(10)) is 37.

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If f(x) = x² + 1 and g(x) = x - 4, which value is equivalent to f(g(10))?

Summary:

If f(x) = x² + 1 and g(x) = x - 4, then the value equivalent to f(g(10)) is 37.