Basic Math/algebra

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Question
Hello Pawan:
Could you solve this problem for me algebraically:
g(x)= 3f(x+1)-2 and also if you could list the transformations of f(x)= x^3-2x+x to obtain g(x)
Thank you.
Angelo

Answer
Angelo,

f(x) = x^3-2x+x
Hence f(x+1) = (x+1)^3 - 2(x+1) + (x+1)  ....... (Replacing x with x+1 in f(x))
f(x+1) = [x^3 + 1^3 + 3*x^2*1+ 3*x*1^2] - 2x-2 +x+1 ...... [(a + b)^3 = a^3 + b^3 + 3ab(a + b)]
= x^3 + 1 + 3x^2 + 3x
= x^3 + 3x^2 + 3x +1  ..........(After rearranging above equation)

Thus we get, f(x+1) = x^3 + 3x^2 + 3x +1 ...................................(1)

Now, g(x)= 3f(x+1)-2
Putting value of f(x+1) from equation (1) above in g(x), we get,

g(x) = 3(x^3 + 3x^2 + 3x +1) - 2
g(x) = 3x^3 + 9x^2 + 9x + 3 - 2
g(x) = 3x^3 + 9x^2 + 9x + 1       ................................(2)

I hope that this is clear. Please let me know if you need further clarification.

All the best!
Regards,
Pawan

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Pawan Musale

Expertise

I can answer Basic Mathematics questions like: Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc I can try to answer questions of probability and set theory

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Tutoring on allexperts.com since long time

Education/Credentials
I am Bachelor of Engineering (Instrumentation) from the reputed institute in India.

Awards and Honors
I was 18th in High School Scholarship examination in Maharashtra State of India. I was second in Mathematics in Maharashtra State in Secondary School Certificate examination.

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