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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 $t(C) = 212$.
Solution :
Step 1: Establishing the Governing Equation
The relationship between temperature in degrees Celsius ($C$) and degrees Fahrenheit ($F$) is provided by the linear function:
$t(C) = \frac{9}{5}C + 32$
where $t(C)$ represents the temperature in degrees Fahrenheit. [Per the definition of the linear temperature conversion function].
Step 2: Substituting the Known Variable
We are given that the temperature in Fahrenheit is $t(C) = 212$. We substitute this value into the governing equation to solve for the unknown variable $C$:
$212 = \frac{9}{5}C + 32$
Step 3: Algebraic Isolation of the Variable $C$
To isolate the term containing $C$, we apply the subtraction property of equality by subtracting 32 from both sides of the equation:
$212 - 32 = \frac{9}{5}C$
$180 = \frac{9}{5}C$
Step 4: Solving for $C$
To isolate $C$, multiply both sides of the equation by the reciprocal of the coefficient $\frac{9}{5}$, which is $\frac{5}{9}$:
$C = 180 \times \frac{5}{9}$
$C = \left(\frac{180}{9}\right) \times 5$ [By the Associative Property of Multiplication]
$C = 20 \times 5$
$C = 100$
Visual Representation of the Linear Relationship
Final Solution: The value of $C$ when $t(C) = 212$ is $100^{\circ}\text{C}$.
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) $f(7)$
- 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) $t(–10)$
- 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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