Question

- If f ( x ) = x² + 2x - 1 and g ( x ) = 3x - 2 , then verify the following :

1.
`\large{ \bf{( (f)/(g))(2) = (f(2))/(g(2)) }}`
- Irrelevant / Random answers will be reported! *​

Answer 1

Explanation:

• f(x) = x² + 2x - 1
• g(x) = 3x - 2

Soo :

`\tt( (f)/(g) )(2) = (f(2))/(g(2))`

`\tt( \frac{ {x}^(2) + 2x - 1 }{3x - 2} )(2) = \frac{ {2}^(2) + 2(2) - 1 }{3(2) - 2}`

`\tt( \frac{ {2}^(2) + 2(2) - 1}{3(2) - 2} )= (7)/(4)`

`\boxed{ \tt (7)/(4) = (7)/(4) }`

Soo true.

Answer 2

Explanation:

Hey there!

Given;

f ( x ) = x² + 2x - 1

g ( x ) = 3x - 2

To verify:

`( (f)/(g) )(2) = (f(2))/(g(2))`

LHS:

`((f)/(g) )(x) = \frac{ {x}^(2) + 2x - 1}{3x - 2}`

~ Insert "2" instead of "x".

`((f)/(g) )(2) = \frac{ {2}^(2) + 2 * 2 - 1 }{3 * 2 - 2}`

Simplify it;

`(f)/(g) (2) = (4 + 4 - 1)/(6 - 2)`

Therefore; (f/g)(2) = 7/4.

RHS:

`(f(x))/(g(x)) = \frac{ {x}^(2) + 2x - 1}{3x - 2}`

~Insert "2" instead of"x".

`(f(2))/(g(2)) = \frac{ {2}^(2) + 2 * 2 - 1 }{3 * 2 - 2}`

Simplify it.

`(f(2))/(g(2)) = (4 + 4 - 1)/(6 - 2)`

Therefore, f(2)/g(2) = 7/4.

Since (f/g)(2) = f(2)/g(2) = 7/4.

Proved!

Hope it helps!