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Q3(iii):
A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (iii) $f(–3)$
Solution :
Step 1: Identifying the Function Definition
The function is explicitly defined as a linear mapping $f: \mathbb{R} \to \mathbb{R}$ given by the algebraic expression:
$f(x) = 2x - 5$ [Given functional rule]
Step 2: Substitution of the Independent Variable
To determine the value of the function at a specific point $x = c$, we substitute the value $c$ into the variable $x$ within the expression. For the requested value $f(-3)$, we set $x = -3$.
$f(-3) = 2(-3) - 5$ [By the principle of functional substitution]
Step 3: Algebraic Evaluation
Perform the multiplication followed by the subtraction as dictated by the order of operations (PEMDAS/BODMAS):
- First, calculate the product: $2 \times (-3) = -6$ [By the property of multiplication of integers]
- Next, evaluate the final expression: $-6 - 5 = -11$ [By the property of subtraction of signed numbers]
Visual Representation of the Linear Function
Summary of Calculation
| Input ($x$) | Substitution | Output ($f(x)$) |
|---|---|---|
| $-3$ | $2(-3) - 5$ | $-11$ |
Final Solution: $f(-3) = -11$
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(ii): A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (ii) $f(7)$
- 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
Chapters in CBSE - Class 11 Mathematics
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