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2 years ago

If h(x) is the inverse of f(x), what is the value of h(f(x))? OO 0 1 f(x)

Mathematics

2 answers:

kozerog [31]2 years ago

8 0

Answer:

Step-by-step explanation:

h(f(x) = x.

For example the inverse of f(x) = 2x is g(x) = x/2

f((gx)) 2 (x/2)

= 2x / 2

= x.

butalik [34]2 years ago

5 0

<h2>Answer:</h2>

If h(x) is the inverse of f(x), then the value of h(f(x)) is:

<h2>Step-by-step explanation:</h2>

Inverse of a function-

The inverse of a given function is a function which reverses the action of the other function.

Also, the composition of a function and it's inverse no matter in which order they are applied always gives us the identity function.

( Identity function-- Identity function is a function which when applied to some other function always retains that function )

i.e. If h(x) is the inverse of f(x) ; then we have:

$h(f(x))=f(h(x))=x$

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DanielleElmas [232]

Answer:

Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that $csc(x)=1/sin(x)$ and $sec(x)=1/cos(x)$ .

Thus:

$\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}$

$=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }$

Let's do the first part first: (Recall how to divide fractions)

$\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}$

For the second term:

$\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}$

So, all together: (same denominator; combine terms)

$\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}$

Note the numerator; it can be derived from the Pythagorean Identity:

$sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)$

Thus, we can substitute the numerator:

$\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1$

Everything simplifies to 1.

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2 years ago

Why are triangles congruent ?

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a motorist left home at 10 a.m. to travel to a cityof a distance of 260 km he reckoned hecould average 80km/ h at what time woul

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Answer:

He would get there at 1:15 (I did this in my head, may be wrong)

Step by step solution:

We know the motorist left home at 10. We can divide the 260/80 and we get 3 hrs, we still have 20 km left over, keep on dividing and you get 1:15 p.m.

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