Question

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Answer 1

Answer:

Given: f(x) = √x and g(x) = ( 7x + b )

It is given y = f [ g(x) ] where the plane passes through the point ( 4,6 ).

By the point we get that: x = 4 and y = 6

Now we  have to find value of 'b' based on the given information.

f [ g(x) ] is generally known as a composite function. For better understanding, let us represent g(x) as 'A'.

Now our composite function changes into: f [ A ].

It is given that y = f [ A ]

⇒ 6 = f [ A ]

Now f ( x ) gives √x, therefore f ( A ) should give us √A.

⇒ 6 = √(A)   ... Eqn. (1)

We have taken g(x) = A. Therefore substituting value of g(x) we get:

⇒ A = 7x + b

Substituting this in Eqn. (1) we get:

⇒ 6 = √(7x + b)

Squaring on both sides we get:

⇒ 36 = 7x + b

We are given that 'x' is equal to 4. Hence substituting x as 4 we get:

⇒ 36 = 7(4) + b

⇒ 36 = 28 + b

⇒ b = 36 - 28

⇒ b = 8

Hence the value of 'b' is 8.

Hence Option (A) is correct.