Question

If h(3x+2)=6x+11,Find h(x)​

Answer 1

Answer:

h(X) = -3

Step-by-step explanation:

3x + 2 = 6x + 11

3x - 6x = 11 - 2

-3x = 9

x = -9/3

x = -3

Answer 2

Given :-

• h (3x + 2) = 6x + 11

To Find :-

• h(x)

Solution :-

Given that,

$\rm :\longmapsto\:h(3x + 2) = 6x + 11 - - (1)$

$\red{\rm :\longmapsto\:Let \: 3x + 2 = y}$

$\red{\rm :\longmapsto\:3x = y - 2}$

$\red{\rm :\longmapsto\:x = \dfrac{y - 2}{3} }$

So, equation (1) can be rewritten as

$\rm :\longmapsto\:h(y) = 6\bigg(\dfrac{y - 2}{3} \bigg) + 11$

$\rm :\longmapsto\:h(y) = 2(y - 2) + 11$

$\rm :\longmapsto\:h(y) = 2y - 4 + 11$

$\rm :\longmapsto\:h(y) = 2y + 7$

Now, Replace y by x, we get

$\rm :\longmapsto\:h(x) = 2x + 7$

Hence,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \red{\boxed{\bf :\implies\:h(x) = 2x + 7}}$

Additional Information :-

One - one Function or Injective Function:-

• A function f from A to B is called one - one if distinct elements of A have distinct images in B.

Onto Function or Surjective Function : -

• A function from A to B is called onto if every element of B has atleast one pre - image in A.

Bijective Function :-

• A function is Bijective if it is one - one as well as onto.