If  
f
(
x
)
=
x
4
+
8
,
g
(
x
)
=
x
−
8
and
h
(
x
)
=
√
x
 , then

f
(
g
(
h
(
x
)
)
)
 =

We are given three functions: 

- \( f(x) = x^4 + 8 \)
- \( g(x) = x - 8 \)
- \( h(x) = \sqrt{x} \)

We are tasked with finding \( f(g(h(x))) \). This means we will substitute \( h(x) \) into \( g(x) \), then substitute that result into \( f(x) \). Let's solve this step-by-step:

### Step 1: Compute \( h(x) \)
\[
h(x) = \sqrt{x}
\]

### Step 2: Compute \( g(h(x)) \)
Substitute \( h(x) = \sqrt{x} \) into \( g(x) \):
\[
g(h(x)) = g(\sqrt{x}) = \sqrt{x} - 8
\]

### Step 3: Compute \( f(g(h(x))) \)
Now, substitute \( g(h(x)) = \sqrt{x} - 8 \) into \( f(x) \):
\[
f(g(h(x))) = f(\sqrt{x} - 8) = (\sqrt{x} - 8)^4 + 8
\]

Thus, the expression simplifies to:
\[
f(g(h(x))) = (\sqrt{x} - 8)^4 + 8
\]

This is the final expression for \( f(g(h(x))) \).

Would you like to expand this further or need a detailed breakdown of how to expand \( (\sqrt{x} - 8)^4 \)?

---

**Related Questions:**

1. What happens if we evaluate \( f(g(h(16))) \)?
2. How would the function \( f(g(x)) \) change if \( g(x) = x + 8 \)?
3. What is the domain of \( h(x) = \sqrt{x} \)?
4. How can \( (\sqrt{x} - 8)^4 \) be expanded?
5. How would we find \( f(g(x)) \) if \( f(x) \) were a different function, such as \( f(x) = x^3 + 8 \)?

**Tip:** When dealing with compositions of functions, always start from the innermost function and work your way outward step by step.

If f(x) = x^4 + 8, g(x) = x - 8 and h(x) = √x, then f(g(h(x))) =

Learn how to solve the function composition problem f(g(h(x))) where f(x) = x^4 + 8, g(x) = x - 8, and h(x) = √x. This step-by-step guide covers key algebraic concepts, including radicals and polynomials, and is suitable for students in Grades 10-12.

Math Problem Statement

If
f ( x )

x 4 + 8 , g ( x )

x − 8 and h ( x )

f ( g ( h ( x ) ) )

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation