Answer :
Answer:
y = (1/4)x
Explanation:
f(x) = 4x or y = 4x
Its inverse is obtained by switching the variables and solving for y.
x = 4y
y = (1/4)x
For clarity, the question is formatted as follows:
Which represents the inverse of the function f(x) = 4x?
i. h(x) = x + 4
ii. h(x) = x – 4
iii. h(x) = three-quarters x
iv. h(x) = one-quarter x
Option (iv) i.e h(x) = one-quarter x gives the correct answer.
The inverse of a function f(x) is the function, say g(x), that reverses the operations performed on f(x).
Some operations and their inverse are as follows;
i. addition (+) is the inverse of subtraction (-) and vice-versa.
ii. multiplication (×) is the inverse of division (÷) and vice-versa.
iii. cos⁻¹ x is the inverse of cos x and vice-versa
iii. sin⁻¹ x is the inverse of sin x and vice-versa
iii. cos⁻¹ x is the inverse of tan x and vice-versa
For example, if
f(x) = 3x
this means that f(x) is given by multiplying x by 3 to give 3x.
To reverse this function f(x) = 3x, we simply perform a division by 3 on x rather than a multiplication by 3 since division is the reverse of multiplication.
Therefore, g(x) which is the inverse of f(x) is given by;
g(x) = [tex]\frac{x}{3}[/tex]
This can be re-written as;
g(x) = [tex]\frac{1}{3}x[/tex]
In other words, the inverse of the function f(x) = 3x, is the function g(x) which is one-third of x
Now, to solve the given question;
f(x) = 4x.
This means that f(x) is given by multiplying x by 4 to give 4x.
To find the inverse of f(x) = 4x, simply perform a division by 4 on x.
Therefore, h(x) which is the inverse of f(x) is given by;
h(x) = [tex]\frac{x}{4}[/tex]
h(x) = [tex]\frac{1}{4}x[/tex]
Therefore, the inverse of the function f(x) = 4x, is the function g(x) which is one-quarter of x (or one-quarter x).
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