Given $f (x) = 3 x - 1, g (x) = x^{2} - 7, h (x) = x^{4}$ $f(x)=3x-1, g(x)=x^2-7, h(x)=x^4$ , how do you find $f (g (h (x))$ $f(g(h(x))$ ?

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Given $f (x) = 3 x - 1, g (x) = x^{2} - 7, h (x) = x^{4}$ $f(x)=3x-1, g(x)=x^2-7, h(x)=x^4$ , how do you find $f (g (h (x))$ $f(g(h(x))$ ?

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Answer 1 · 2016-12-17T22:03:32

$3 x^{8} - 22$ $3x^8-22$

Explanation:

To evaluate $f (g (h (x))$ $f(g(h(x))$ first evaluate $g (h (x))$ $g(h(x))$ That is the 'inner' function.

To evaluate g(h(x)) substitute $x = x^{4}$ $x=x^4$ into g(x))

$\Rightarrow g (h (x)) = {(x^{4})}^{2} - 7 = x^{8} - 7$ $rArrg(h(x))=(x^4)^2-7=x^8-7$

Now to evaluate f(g(h(x)) substitute $x = x^{8} - 7$ $x=x^8-7$ into f(x)

$\Rightarrow f (g (h (x)) = f (x^{8} - 7) - 1 = 3 (x^{8} - 7) - 1$ $rArrf(g(h(x))=f(x^8-7)-1=3(x^8-7)-1$

$= 3 x^{8} - 21 - 1 = 3 x^{8} - 22$ $=3x^8-21-1=3x^8-22$

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Given $f (x) = 3 x - 1, g (x) = x^{2} - 7, h (x) = x^{4}$ $f(x)=3x-1, g(x)=x^2-7, h(x)=x^4$ , how do you find $f (g (h (x))$ $f(g(h(x))$ ?

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Given f(x)=3x−1,g(x)=x2−7,h(x)=x4f(x)=3x-1, g(x)=x^2-7, h(x)=x^4, how do you find f(g(h(x))f(g(h(x))?

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Given $f (x) = 3 x - 1, g (x) = x^{2} - 7, h (x) = x^{4}$ $f(x)=3x-1, g(x)=x^2-7, h(x)=x^4$ , how do you find $f (g (h (x))$ $f(g(h(x))$ ?