If A = {1,2,3,4} and B = {1,4,9,16,25} is a function f is defined set A to B where f(x) = x^2 then the range of f is:

Option b: {1,4,9,16}. Solution: The range of a function f: A to B is the set of all image values of the elements of the domain A under f. Given: Domain A = {1, 2, 3, 4} Function formula: f(x) = x^2 We compute the image for each element in the domain: f(1) = 1^2 = 1 f(2) = 2^2 = 4 f(3) = 3^2 = 9 f(4) = 4^2 = 16 The set of these image values is: text{Range}(f) = {1, 4, 9, 16} Hence, Option B is the correct answer.

If $A = \{1,2,3,4\}$ and $B = \{1,4,9,16,25\}$ is a function $f$ is defined set $A$ to $B$ where $f(x) = x^2$ then the range of $f$ is:

The correct answer is Option b: $\{1,4,9,16\}$. The range of a function $f: A \to B$ is the set of all image values of the elements of the domain $A$ under $f$. Given: Domain $A = \{1, 2, 3, 4\}$ Function formula: $f(x) = x^2$ We compute the image for each element in the domain: $$f(1) = 1^2 = 1$$ $$f(2) = 2^2 = 4$$ $$f(3) = 3^2 = 9$$ $$f(4) = 4^2 = 16$$ The set of these image values is: $$\text{Range}(f) = \{1, 4, 9, 16\}$$ Hence, **Option B** is the correct answer.

Set, Relations and FunctionsPYQ Nov 18, MTP May 19Question 1983 of 217

All Questions

If $\displaystyle A = \{1,2,3,4\}$ and $\displaystyle B = \{1,4,9,16,25\}$ is a function $\displaystyle f$ is defined set $\displaystyle A$ to $\displaystyle B$ where $\displaystyle f(x) = x^2$ then the range of $\displaystyle f$ is:

Options

\displaystyle \{1,2,3,4\}

\displaystyle \{1,4,9,16\}

\displaystyle \{1,4,9,16,25\}

DNone of these

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Correct Answer

✅ Option b — $\displaystyle \{1,4,9,16\}$

All Options:

A $\displaystyle \{1,2,3,4\}$
B $\displaystyle \{1,4,9,16\}$
C $\displaystyle \{1,4,9,16,25\}$
DNone of these

Detailed Solution & Explanation

The range of a function

\displaystyle f: A \to B

is the set of all image values of the elements of the domain

\displaystyle A

under

\displaystyle f

.

Given:
Domain

\displaystyle A = \{1, 2, 3, 4\}

Function formula:

\displaystyle f(x) = x^2

We compute the image for each element in the domain:

f(1) = 1^2 = 1

f(2) = 2^2 = 4

f(3) = 3^2 = 9

f(4) = 4^2 = 16

The set of these image values is:

\text{Range}(f) = \{1, 4, 9, 16\}

Hence, **Option B** is the correct answer.

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If A={1,2,3,4}\displaystyle A = \{1,2,3,4\}A={1,2,3,4} and B={1,4,9,16,25}\displaystyle B = \{1,4,9,16,25\}B={1,4,9,16,25} is a function f\displaystyle ff is defined set A\displaystyle AA to B\displaystyle BB where f(x)=x2\displaystyle f(x) = x^2f(x)=x2 then the range of f\displaystyle ff is: