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iris [78.8K]
3 years ago
5

Please help with these 2 questions! Thank you

Mathematics
1 answer:
irga5000 [103]3 years ago
3 0

Answer:

15. h⁻¹ (x) = 5x-6/2

16. (g.f)x = 4x^2 -2x -1

Step-by-step explanation:

15. Find Inverse of h(x) =  2x+6 /5

Let y = 2x+6/5 we need to find value of x

Multiplying both sides with 5

5y = 2x+6

Adding -6 on both sides

5y -6 = 2x

Dividing both sides by 2

5y-6/2 = x

Now replace y with x our answer will be:

h⁻¹ (x) = 5x-6/2

16. f(x) =2x-1 and g(x) = x^2 -2 find (g.f)x

(g.f)x can be written as: g(f(x))

We know f(x) = 2x-1 so, put value of f(x) into x of g(x).

Putting values we get:

(g.f)x = g(f(x))= (2x-1)^2 -2

                   = 4x^2 -2x +1 -2

                   = 4x^2 -2x -1

               

so, (g.f)x = 4x^2 -2x -1

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dy/dx by implicit differentiation is cos(πx)/sin(πy)

<h3>How to find dy/dx by implicit differentiation?</h3>

Since we have the equation

(sin(πx) + cos(πy)⁸ = 17, to find dy/dx, we differentiate implicitly.

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8[(sin(πx) + cos(πy)]⁷ ×  (πcos(πx) - πsin(πy) × dy/dx) = 0

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So, dy/dx by implicit differentiation is cos(πx)/sin(πy)

Learn more about implicit differentiation here:

brainly.com/question/25081524

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