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kap26 [50]
3 years ago
11

What is the inverse of the function h(x)=\dfrac{5}{2}x+4h(x)= 2 5 ​ x+4h, left parenthesis, x, right parenthesis, equals, start

fraction, 5, divided by, 2, end fraction, x, plus, 4?\
Mathematics
2 answers:
Phantasy [73]3 years ago
6 0

Answer:

The inverse of the function h(x) is h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}.

Step-by-step explanation:

The given function is

h(x)=\dfrac{5}{2}x+4

Replace h(x) by y.

y=\dfrac{5}{2}x+4

Interchange x and y.

x=\dfrac{5}{2}y+4

Subtract 4 from both sides to isolate variable y,

x-4=\dfrac{5}{2}y

Multiply both sides by 2.

2x-8=5y

Divide both sides by 5.

\frac{2}{5}x-\frac{8}{5}=y

Replace y by h⁻¹(x).

h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}

Therefore the inverse of the function h(x) is h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}.

photoshop1234 [79]3 years ago
5 0

Answer:

b, 3/2

Step-by-step explanation:

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