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Q3(ii):
A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (ii) $f(7)$
Solution :
Step 1: Identifying the Functional Definition
The given function is defined as a mapping $f: \mathbb{R} \to \mathbb{R}$ such that the rule for the transformation of any element $x$ in the domain is:
$f(x) = 2x - 5$
[Definition of a linear function in terms of its algebraic expression]
Step 2: Substitution of the Independent Variable
To determine the value of the function at $x = 7$, we substitute the value $7$ into the expression for $f(x)$.
$f(7) = 2(7) - 5$
[Substitution Property of Equality]
Step 3: Arithmetic Evaluation
Perform the operations following the Order of Operations (PEMDAS/BODMAS):
- Multiply the scalar coefficient by the input value: $2 \times 7 = 14$
- Subtract the constant term: $14 - 5 = 9$
Step 4: Final Verification
The calculation $f(7) = 2(7) - 5 = 14 - 5 = 9$ confirms that the image of the element $7$ under the function $f$ is $9$.
Final Solution: $f(7) = 9$
More Questions from Class 11 Mathematics Relations and Functions EXERCISE 2.3
- Q1(i): Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) \{(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)\}
- Q1(ii): Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (ii) \{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)\}
- Q1(iii): Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (iii) \{(1,3), (1,5), (2,5)\}
- Q2(i): Find the domain and range of the following real functions: (i) $f(x) = –|x|$
- Q2(ii): Find the domain and range of the following real functions: (ii) $f(x) = \sqrt{9-x^2}$.
- Q3(i): A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (i) $f(0)$
- Q3(iii): A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (iii) $f(–3)$
- Q4(i): The function ‘$t$’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find (i) $t(0)$
- Q4(ii): The function ‘$t$’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find (ii) $t(28)$
- Q4(iii): The function ‘$t$’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find (iii) $t(–10)$
- Q4(iv): The function ‘$t$’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find (iv) The value of $C$, when $t(C) = 212$.
- Q5(i): Find the range of each of the following functions. (i) $f(x) = 2 – 3x, x \in \mathbb{R}, x > 0$.
- Q5(ii): Find the range of each of the following functions. (ii) $f(x) = x^2 + 2$, $x$ is a real number.
- Q5(iii): Find the range of each of the following functions. (iii) $f(x) = x$, $x$ is a real number.
CBSE Solutions for Class 11 Mathematics Relations and Functions
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