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NARA [144]
2 years ago
11

I need to multi-step function inverse, photo included

Mathematics
1 answer:
STALIN [3.7K]2 years ago
4 0

Answer:

f^{-1} = (9x + 1)^{7}

Step-by-step explanation:

y\:=\:\frac{x^{\frac{1}{7}}-1}{9}

replace x with y:

x=\frac{y^{\frac{1}{7}}-1}{9}

solve for y:

9x=y^{\frac{1}{7}}-1}

9x + 1 = y^{\frac{1}{7} }

y = (9x + 1)^{7}

therefore:

f^{-1} = (9x + 1)^{7}

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then csc(</span>θ) = 257, but csc(θ) = \frac{1}{sin(θ)} = 257
==> sin(<span>θ) = \frac{1}{257}
it is positive, so now we can determine that is in Quadrant 2

sin(</span>θ) = opp./hyp both of opp and hyp are positive but adj suppose to negative because that way it leads the cos(<span>θ) < 0
</span>cos(<span>θ) = adj/hyp
</span>Pythereom to find the adj: 257^{2} -  1^{2}  = adj ==\ \textgreater \  adj  \sqrt{ 257^{2} -   1^{2} } ==\ \textgreater \  adj = 16 \sqrt{258}

cosθ = \frac{16 \sqrt{258} }{257} &#10;
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Below.

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