Work out the inverse function for each equation.
a) $y = 2 x + 5$
b) $y = 4 x - 7$
c) $y = \frac{x}{2} + 1$
d) $y = \frac{x - 4}{3}$

Open in App

Solution

# Inverse functions.
(A) $y = 2 x + 5 \Rightarrow y - 5 = 2 x \Rightarrow x = \frac{y - 5}{2}$
(B) $y = 4 x - 7 \Rightarrow 4 x = y + 7 \Rightarrow x = \frac{y + 7}{4}$
(C) $y = x / 2 + 1 \Rightarrow \frac{x}{2} = y - 1 \Rightarrow x = 2 y - 2$
(D) $y = \frac{x - 4}{3} \Rightarrow x - 4 = 3 y \Rightarrow x = 3 y + 4$

Suggest Corrections

Similar questions

Q. Let

A = 1, 2, 3, 4, 5

B = 1, 3, 5, 7, 9, 10, 17, 26, 30 .

Which of the following sets of ordered pairs are (i) relations (ii) functions (iii) neither, from A to B
(a)

R_{1}

= {(1, 3), (3, 3), (5, 17), (1, 2)}
(b)

R_{2}

= {(3, 7), (4, 5), ( 5, 30)}
(c)

R_{3} = (x, y) : x \in A, y \in B, x + y = 8

(d)

R_{4} = (x, y) : x \in A, y \in B, y = x^{2} + 1

(e)

R_{5} = (x, y) : x \in A, y \in B, y = 2 x - 1

Which of the pairs given in options will add up to give $9 x + 5 y$ ?

Q. Subtract:
(i) 5a + 7b − 2c from 3a − 7b + 4c
(ii) a − 2b − 3c from −2a + 5b − 4c
(iii) 5x² − 3xy + y² from 7x² − 2xy − 4y²
(iv) 6x³ − 7x² + 5x − 3 from 4 − 5x + 6x² − 8x³
(v) x³ + 2x²y + 6xy² − y³ from y³ − 3xy² − 4x²y
(vi) −11x²y² + 7xy −6 from 9x²y² −6xy + 9
(vii) −2a + b + 6d from 5a − 2b − 3c

Simplify each of the following: $(i) x^{2} - 3 x + 5 - \frac{1}{2} (3 x^{2} - 5 x + 7) (i i) [5 - 3 x + 2 y - (2 x - y)] - (3 x - 7 y + 9) (i i i) \frac{11}{2} x^{2} y - \frac{9}{4} x y^{2} + \frac{1}{4} x y - \frac{1}{14} y^{2} x + \frac{1}{15} y x^{2} + \frac{1}{2} x y (i v) (\frac{1}{3} y^{2} - \frac{4}{7} y + 11) - (\frac{1}{7} y - 3 + 2 y^{2}) - (\frac{2}{7} y - \frac{2}{3} y^{2} + 2) (v) - \frac{1}{2} a^{2} b^{2} c + \frac{1}{3} a b^{2} c - \frac{1}{4} a b c^{2} - \frac{1}{5} c b^{2} a^{2} + \frac{1}{6} c b^{2} a - \frac{1}{7} c^{2} a b + \frac{1}{8} c a^{2} b .$

Factorize:

$12 (x + y)^{2} - (x + y) - 35$

Join BYJU'S Learning Program

Work out the inverse function for each equation.a)y=2x+5b)y=4x−7c)y=x2+1d)y=x−43

# Inverse functions.(A) y=2x+5⇒y−5=2x⇒x=y−52(B) y=4x−7⇒4x=y+7⇒x=y+74(C) y=x/2+1⇒x2=y−1⇒x=2y−2(D) y=x−43⇒x−4=3y⇒x=3y+4

Work out the inverse function for each equation.
a) $y = 2 x + 5$
b) $y = 4 x - 7$
c) $y = \frac{x}{2} + 1$
d) $y = \frac{x - 4}{3}$