Questions: If f(x)=x^4+6, g(x)=x-6 and h(x)=sqrt(x), then f(g(h(x)))=

Transcript text: If $f(x)=x^{4}+6, g(x)=x-6$ and $h(x)=\sqrt{x}$, then \[ f(g(h(x)))= \]

Solution

Step 1: Compute $ h(x) $

Given $ h(x) = \sqrt{x} $, we start by evaluating $ h(x) $: \[ h(x) = \sqrt{x}. \]

Step 2: Compute $ g(h(x)) $

Next, substitute $ h(x) $ into $ g(x) $: \[ g(h(x)) = g(\sqrt{x}) = \sqrt{x} - 6. \]

Step 3: Compute $ f(g(h(x))) $

Finally, substitute $ g(h(x)) $ into $ f(x) $: \[ f(g(h(x))) = f(\sqrt{x} - 6) = (\sqrt{x} - 6)^4 + 6. \]

The composition $ f(g(h(x))) $ is: \[ \boxed{f(g(h(x))) = (\sqrt{x} - 6)^4 + 6}. \]

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