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nordsb [41]
3 years ago
15

If h(x) is the inverse of f(x), what is the value of h(f(x))?.

Mathematics
2 answers:
Marysya12 [62]3 years ago
7 0
To answer the question above, make use of one of the definitions of the inverse functions. If h(x) and f(x) are inverses of each other, then applying the operation, h(f(x)) will give back the value of the initial value. Therefore, the answer is x. 
nikklg [1K]3 years ago
5 0

Answer:

Step-by-step explanation:

Given that h(x) is inverse of f(x0)

As per definition of inverse functions we find that always

f*f inverse = f inverse * f = I = identity function x

Hence here also since h is given to inverse of f we will get composition of functions h and f giving answer as x.

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Suppose that \nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}. if f(0,0,0) = 2, find f(1,1,1).
lesya [120]

The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted C, which we can parameterize by the vector-valued function,

\mathbf r(t)=(1-t)(\mathbf i+\mathbf j+\mathbf k)

for 0\le t\le1, which has differential

\mathrm d\mathbf r=-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt

Then with x(t)=y(t)=z(t)=1-t, we have

\displaystyle\int_{\mathcal C}\nabla f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\nabla f(x(t),y(t),z(t))\cdot\mathrm d\mathbf r

=\displaystyle\int_{t=0}^{t=1}\left(2(1-t)^3e^{(1-t)^2}\,\mathbf i+(1-t)e^{(1-t)^2}\,\mathbf j+(1-t)e^{(1-t)^2}\,\mathbf k\right)\cdot-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt

\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)(t^2-2t+2)\,\mathrm dt

Complete the square in the quadratic term of the integrand: t^2-2t+2=(t-1)^2+1=(1-t)^2+1, then in the integral we substitute u=1-t:

\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)((1-t)^2+1)\,\mathrm dt

\displaystyle=-2\int_{u=0}^{u=1}e^{u^2}u(u^2+1)\,\mathrm du

Make another substitution of v=u^2:

\displaystyle=-\int_{v=0}^{v=1}e^v(v+1)\,\mathrm dv

Integrate by parts, taking

r=v+1\implies\mathrm dr=\mathrm dv

\mathrm ds=e^v\,\mathrm dv\implies s=e^v

\displaystyle=-e^v(v+1)\bigg|_{v=0}^{v=1}+\int_{v=0}^{v=1}e^v\,\mathrm dv

\displaystyle=-(2e-1)+(e-1)=-e

So, we have by the fundamental theorem of calculus that

\displaystyle\int_C\nabla f(x,y,z)\cdot\mathrm d\mathbf r=f(1,1,1)-f(0,0,0)

\implies-e=f(1,1,1)-2

\implies f(1,1,1)=2-e

3 0
3 years ago
3x + 12+ 9x - 72<br><br><br>Solve?​
Reil [10]

Answer:

12x - 60

Step-by-step explanation:

3x+12+9x-72\\=3x+9x+12-72\\=12x+12-72\\=12x-60

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2 years ago
I need the answer please asp
11Alexandr11 [23.1K]

Answer:

The answer is a isosceles right I think.

8 0
2 years ago
The picture below shows a right-triangle-shaped charging stand for a gaming system:
Kobotan [32]

Answer:

The answer is between first option and last option.

Step-by-step explanation:

That my Contributions to this questions

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3 years ago
Geometry help needed! Thanks.
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EN = NE

Answer

D. last one

NE

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