Question

If f(x) = 3x - 2 and fog(x) = 6x - 2, find g(x).



Step by Step Explanation Required
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Answer 1

Answer:

2x

Step By Step Explanation:

Given:

f(x) = 3x - 2

fog(x) = 6x - 2

To find: g(x) = ?

Now,

Let g(x) = y then,

∴ fog(x) = 6x - 2

⇒ f(g(x)) = 6x - 2

⇒ f(y) = 6x - 2

⇒ 3y - 2 = 6x - 2

⇒ 3y = 6x - 2 + 2

⇒ 3y = 6x

⇒ y = 6x/3

∴ y = 2x

Hence, The required value of g(x) is 2x.

Answer 2

Answer:

$\boxed{\boxed{\bf{\red{g(x)=2x}}}}$

Step-by-step explanation:

Given that :-

f(x) = 3 x - 2

This is called a polynomial function .

Here f(x) is a function and x is a variable which determines the function's value .

fog(x) = 6 x - 2

This can also be written as :-

f(g(x)) = 6 x - 2

⇒ f(g(x)) = 3(2x) - 2

Hence g(x) must be 2x since f(x) = 3 x - 2

Alternative method exist .

We can take another variable for example : y in order to find g(x)

f(x) = 3 x - 2

f(g(x)) = 6 x - 2

⇒ f(y) = 6 x - 2

⇒ 3 y - 2 = 6 x - 2

⇒ 3 y = 6 x

⇒ y = 6 x/3

⇒ y = 2 x

Hence the value of g(x) will be 2 x .

MORE INFO :-

→ A polynomial function f(x) changes as soon as the value of x changes .

→ We need to determine the equation of f(x) in order to find the change .

→ For example given is f(x) = 3 x - 2 . So the value of x if 1 will result in the value of f(x) to be 3-2 = 1

→ If the value of x is 2 : 3(2) - 2 = 6 - 2 = 4 will be the value of the function.

→ Hence we can say that the above function is dependent on the variable x .