Math / Algebra

QuestionChoose the correct answer from those given :
(1) If $f(2) = 4$ , $g(4) = 3$ , then $(g \circ f)(2) =$ ......... (a) 12 (b) 4 (c) 3 (d) 1 Interactive test 1

Studdy Solution

STEP 1

What is this asking? If we apply the function $f$ to the number $2$ , we get $4$ .
If we apply the function $g$ to the number $4$ , we get $3$ .
What do we get if we apply $g$ after applying $f$ to the number $2$ ? Watch out! Don't multiply the results of $f(2)$ and $g(4)$ !
We need to apply $f$ first, then $g$ to the result.

STEP 2

1. Understand Function Composition
2. Evaluate the Composition

STEP 3

Function composition, denoted by $(g \circ f)(x)$ , means applying $f$ to $x$ first, and then applying $g$ to the result.
Think of it like a chain reaction!

STEP 4

In our case, $(g \circ f)(2)$ means we first find $f(2)$ , and then we plug that result into $g$ .

STEP 5

We are given that $f(2) = 4$ .
This means when we plug $2$ into $f$ , we get $4$ .
This is our intermediate result.

STEP 6

Next, we need to find $g(f(2))$ , which is the same as $g(4)$ since $f(2) = 4$ .

STEP 7

We are given that $g(4) = 3$ .
So, when we plug $4$ into $g$ , we get $3$ .
This is our final result!

STEP 8

The answer is (c) $3$ .

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QuestionChoose the correct answer from those given :
(1) If $f(2) = 4$ , $g(4) = 3$ , then $(g \circ f)(2) =$ ......... (a) 12 (b) 4 (c) 3 (d) 1 Interactive test 1

Studdy Solution

STEP 1

STEP 2

1. Understand Function Composition
2. Evaluate the Composition

STEP 3

Function composition, denoted by $(g \circ f)(x)$ , means applying $f$ to $x$ first, and then applying $g$ to the result.
Think of it like a chain reaction!

STEP 4

In our case, $(g \circ f)(2)$ means we first find $f(2)$ , and then we plug that result into $g$ .

STEP 5

We are given that $f(2) = 4$ .
This means when we plug $2$ into $f$ , we get $4$ .
This is our intermediate result.

STEP 6

Next, we need to find $g(f(2))$ , which is the same as $g(4)$ since $f(2) = 4$ .

STEP 7

We are given that $g(4) = 3$ .
So, when we plug $4$ into $g$ , we get $3$ .
This is our final result!

STEP 8

The answer is (c) $3$ .

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QuestionChoose the correct answer from those given :(1) If f(2)=4f(2) = 4f(2)=4, g(4)=3g(4) = 3g(4)=3, then (g∘f)(2)=(g \circ f)(2) =(g∘f)(2)= ......... (a) 12 (b) 4 (c) 3 (d) 1 Interactive test 1

Studdy Solution

STEP 1

STEP 2

1. Understand Function Composition2. Evaluate the Composition

STEP 3

Function composition, denoted by (g∘f)(x)(g \circ f)(x)(g∘f)(x), means applying fff to xxx *first*, and *then* applying ggg to the result.Think of it like a chain reaction!

STEP 4

In our case, (g∘f)(2)(g \circ f)(2)(g∘f)(2) means we *first* find f(2)f(2)f(2), and *then* we plug that result into ggg.

STEP 5

We are given that f(2)=4f(2) = 4f(2)=4.This means when we plug 222 into fff, we get **444**.This is our **intermediate result**.

STEP 6

Next, we need to find g(f(2))g(f(2))g(f(2)), which is the same as g(4)g(4)g(4) since f(2)=4f(2) = 4f(2)=4.

STEP 7

We are given that g(4)=3g(4) = 3g(4)=3.So, when we plug 444 into ggg, we get **333**.This is our **final result**!

STEP 8

The answer is (c) 333.

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QuestionChoose the correct answer from those given :
(1) If $f(2) = 4$ , $g(4) = 3$ , then $(g \circ f)(2) =$ ......... (a) 12 (b) 4 (c) 3 (d) 1 Interactive test 1

1. Understand Function Composition
2. Evaluate the Composition

Function composition, denoted by $(g \circ f)(x)$ , means applying $f$ to $x$ first, and then applying $g$ to the result.
Think of it like a chain reaction!

In our case, $(g \circ f)(2)$ means we first find $f(2)$ , and then we plug that result into $g$ .

We are given that $f(2) = 4$ .
This means when we plug $2$ into $f$ , we get $4$ .
This is our intermediate result.

Next, we need to find $g(f(2))$ , which is the same as $g(4)$ since $f(2) = 4$ .

We are given that $g(4) = 3$ .
So, when we plug $4$ into $g$ , we get $3$ .
This is our final result!

The answer is (c) $3$ .