What is the inverse of f(x)=2.8sin(0.5x-1.5)+12 ?

The inverse of f(x)=2.8sin(0.5x-1.5)+12 is 2arcsin((5(x-12))/(14))+3

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inverse of f(x)=2.8sin(0.5x-1.5)+12

inverse

f (x) = 2.8 sin (0.5 x - 1.5) + 12

2 arcsin (\frac{5 ( x - 12 )}{14}) + 3

Solution steps

Solve for

sin (0.5 x - 1.5), y = 2.8 sin (0.5 x - 1.5) + 12

sin (0.5 x - 1.5) = \frac{5 ( y - 12 )}{14}

sin (a) = b \Rightarrow a = arcsin (b)

0.5 x - 1.5 = arcsin (\frac{5 ( y - 12 )}{14})

Solve for

x, 0.5 x - 1.5 = arcsin (\frac{5 ( y - 12 )}{14})

2 arcsin (\frac{5 ( y - 12 )}{14}) + 3

Substitute

y = x

2 arcsin (\frac{5 ( x - 12 )}{14}) + 3

What is the inverse of f(x)=2.8sin(0.5x-1.5)+12 ?
The inverse of f(x)=2.8sin(0.5x-1.5)+12 is 2arcsin((5(x-12))/(14))+3