Chapter 5: Q 59. (page 257)

If $f (x) = 2 x^{3} - 3 x^{2} + 4 x - 1$ and $g (x) = 2$ , find $(f o g) (x)$ and $(g o f) (x)$ .

Short Answer

Expert verified

The value of $(f o g) (x) = 11$ and $(g o f) (x) = 2$

Step by step solution

Step 1. Given information

The given function $f (x) = 2 x^{3} - 3 x^{2} + 4 x - 1$ and $g (x) = 2$

The function $(f o g) (x) = f (g (x))$

Step 2. Substituteg(x)=2 inf(g(x))

$f (2) = 2 {(2)}^{3} - 3 {(2)}^{2} + 4 (2) - 1 f (2) = 2 (8) - 3 (4) + 8 - 1 f (2) = 16 - 12 + 8 - 1 f (2) = 11$

Step 3. The function(g o f)(x)=g(f(x))Substitute f(x)=2x3-3x2+4x-1in g(x).

$g (2 x^{3} - 3 x^{2} + 4 x - 1) = 2$

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If $f (x) = 2 x^{3} - 3 x^{2} + 4 x - 1$ and $g (x) = 2$ , find $(f o g) (x)$ and $(g o f) (x)$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substituteg(x)=2 inf(g(x))

Step 3. The function(g o f)(x)=g(f(x))Substitute f(x)=2x3-3x2+4x-1in g(x).

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Iff(x)=2x3-3x2+4x-1andg(x)=2, find(fog)(x)and(gof)(x).

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substituteg(x)=2 inf(g(x))

Step 3. The function(g o f)(x)=g(f(x))Substitute f(x)=2x3-3x2+4x-1in g(x).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

If $f (x) = 2 x^{3} - 3 x^{2} + 4 x - 1$ and $g (x) = 2$ , find $(f o g) (x)$ and $(g o f) (x)$ .