Question

If f(x)=2x-5 and g(x)=3x+1 are two functions then find gf^-1 (5).​

Answer 1

Answer:

Hope so that my answer was helpful for you ...........

Answer 2

Value of $\bf \: {gof}^{ - 1}(5) \: is \: \frac{19}{6}$

Given:

• If two functions are
• $f(x) = 2x - 5$ and $g(x) = 3x + 1$

To find:

• Find the value of ${gof}^{ - 1} (5)$

Solution:

Concept to be used:

• Find gof.
• Find inverse of gof.
• put the value in inverse.

Step 1:

Find gof.

Put the value of f(x) in g(x).

$gof(x)= 3(2x - 5) + 1$

or

$gof(x)= 6x - 15 + 1$

or

$\bf gof(x) = 6x - 14$

Step 2:

Find inverse of gof.

Let inverse of gof is y.

So,

$y = 6x - 14$

or

$x = \frac{y + 14}{6}$

or

We can write

$\bf {gof}^{ - 1}(x) = \frac{x + 14}{6}$

Step 3:

Put x= 5

${gof}^{ - 1} (5) = \frac{5 + 14}{6}$

or

$\bf {gof}^{ - 1} (5) = \frac{19}{6}$

Thus,

Value of ${gof}^{ - 1} (5) \: is \: \frac{19}{6}$

Learn more:

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2) If f(x) = 2, g(x) = x², h(x) = 2x for all x ∈ R, then find (fo (goh) (x)).

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