AMCAT Numbers and Divisibility Quiz-1

To find the inverse function, we switch the rolems of x and y and solve for y.

x = \frac{2y-1}{y+4} (switch roles of x and y)
x(y+4) = 2y-1 (multiply both sides by y+4)
xy+4x = 2y-1 (distribute)
xy - 2y = -4x-1 (subtract 2y and add 1 to both sides)
y(x-2) = -4x-1 (factor out y)
y = \frac{-4x-1}{x-2} (divide both sides by x-2)
Therefore, the inverse function of f(x) is f^{-1}(x) = \frac{-4x-1}{x-2}.

a^{m}.a^{n}=a^{m+n}
7+x=11.5
x=4.5

Given expression resembles to
(a^2 - b^2) / (a - b)
(a+b)(a-b) / (a-b)
5.45 + 3.32 = 8.77

To find the inverse of a function, we switch the roles of x and y and solve for y.
So we have x = e^y, which we can solve for y by taking the natural logarithm of both sides, giving us y = ln(x). Therefore, the inverse function is g^{-1}(x) = ln(x).

a^{n}=\frac{1}{a^{-n}}

x−2=−(x−4)
⇒x−2=−x+4
⇒2x=6
=3

5.46 + 2.23 + 1.96
9.65 = 965 / 100 = 193 / 20

To find the inverse of f(x), we switch x and y and solve for y.
Therefore, x = e^{2y}
ln(x) = 2y, and
y = \frac{ln(x)}{2}
Thus, f^{-1}(x) = ln(x)/2

3^{6}=729
x-y=6—-----------------equation(1)
3^{7}=2187
x-y=7—----------------equation(2)

From solving equ. 1 and 2
x=6.5
y=0.5

\frac{5.45 + 6.23 * 9.7}{3.42 + 5.23 * 8.6}
\frac{5.45 + 60.431}{3.42 + 44.978}
\frac{5.45 + 60.431}{3.42 + 44.978}
65.881 / 48.398

To find the inverse of f(x), we switch x and y and solve for y.
Therefore, x = ln(3y)
e^(x) = 3y,
y = e^(x)/3
Thus, f^{-1}(x) = \frac{e^{x}}{3}