GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 61

Answer 1

Given,

$f(x)=ax+b$
$f(bx+a)=x$

Substituting $x$ by $bx+a$
$f(bx+a)=a(bx+a)+b=abx+a^2+b$
$\therefore x=abx+a^2+b$

$a^2+(ab-1)x+b=0$
Above equation will be satisfied only if $a=b=-1$
$\therefore a+b=-1-1=-2$

$\textsf{Option D.}$

Answer 2

Given, $f(x) = ax+b$  -----→ 1

$f(bx + a) = x$  -----→ 2

Using (1), we get

$f(bx + a) = a(bx+a)+b$ ----→ 3

From (2) and (3),

$a(bx + a) + b = x$

=> $abx + a^{2} + b = x$  ---→ 4

Now, put x=0 in (4)

=> $a^{2} + b = 0$  ------→ 5

put x=1 in (4)

$ab + a^{2} + b = 1$

=> $ab = 1$   ---→ (Using 5)

Now, you have 2 equations and 2 variables

$a^{2} + b = 0$

$ab = 1$

Solve the above 2 equations, you will get a = -1 and b = -1

Hence, a + b = -1 + (-1) = -2