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The function f(x) is defined by f(x) = 1 + 2 sin (3x), − π/ 6 ≤ x ≤ π/ 6 . You are given that this function has an inverse, f^ −1 (x). Find f^ −1 (x) and its domain

To find inverse functions we swap the variables of the function we are taking the inverse of. let y=1+2sin(3x)so now, x=1+2sin(3y)Aiming to make y the subject, x-1= 2sin(3y)Therefore, (x-1)/2=sin(3y), 3y= ar...
HC
Answered by Harry C. • Maths tutor
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Comment closely on Stevenson’s presentation of the natural world in one poem from Granny Scarecrow and say how far this poem is characteristic of Stevenson’s style and concerns in the collection

The speaker, presumably Stevenson herself, suggests the importance of nature as a place of home. In the second stanza, the speaker describes the Wrekin as the “homely shape” of a “shell”, suggesting a protec...
HV
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"A chromium compound contains 28.4% sodium and 32.1% chromium by mass, while the rest is oxygen. What is the empirical formula of this compound?"

Start with the definition of empirical formula so we know what we are trying to work out. Empirical formula is the simplest whole-number ratio of elements in a compound. First, let us work out how much of th...
MP
Answered by Mia P. • Chemistry tutor
5807 Views

y = 4sin(x)cos(3x) . Evaluate dy/dx at the point x = pi.

By product rule:u = 4sin(x) v = cos(3x)du/dx = 4cos(x) dv/dx = -3sin(3x)dy/dx = u (dv/dx) + v (du/dx)dy/dx = 4sin(x) * -3sin(3x) + cos(3x) * 4cos(x)dy/dx = -12sin(x)sin(3x) + 4cos(x)cos(3x)Evaluate at x = pi...
WF
Answered by Will F. • Maths tutor
4709 Views

What is a logarithm?

We can explain this by taking a simple power equation such as 2 3 = 8 and setting each number as an unknown variable. For instance 2 3 = x is solved by cubing 2, x 3 = 8 is solved by taking the cube root of ...
DW
Answered by Daniel W. • Maths tutor
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