PizzaMaster Can a one-to-one function have a many-to one inverse function? For example: f(x) = 2x^ 3/4 + 1 has an inverse: f-1(x) = [(x-1) / 2]^ 4/3 How come?
Billzene PizzaMaster If you have f(x) = x0.5 Then f-1(x) = x2, but restricted to the domain R+ u {0}, which means the inverse is also 1-1. The negative branch of x2 isn't a reflection of y = x0.5 in the line y = x, so it's not part of the inverse function
PizzaMaster Ohh so you mean that the range of the original is the domain of the inverse? And so that's why f(x) = 2x^ 3/4 + 1 does have an inverse: f-1(x) = [(x-1) / 2]^ 4/3 BUT with domain [1, infinity)
snowflake How do we know whether the question wants us to give the dilation from x axis or y axis when given both the original and transformed function. For example: f(x)= 1/x2 f1(x)= 5/x2 I got dilation by a factor of 1/5 from the y axis but the answers say factor of 5 from the x axis. Is my answer still valid?
Billzene snowflake Your answer wouldn't be considered correct, if the coefficient of x2 were 5 ie y = 1 / (5x2) then it'd be correct since that would be a dilation from the y-axis
snowflake Billzene Ohh ok but how do we whether to work out it’s dilation from the X or Y axis if it doesn’t say in the question?
Billzene snowflake by recognition of the form y = a/(1/b(x-h))n + k a = dilation factor from x axis b = dilation factor from y axis h = translation in +ve direction of x axis n = power k = translation in the positive direction of y axis This is similar to turning point form of parabolas
chemistry1111 find values of a and b such that a(x+2)+b(x+3)=18x+8 for all values of x if someone could help that would be great
beep_boop_booop chemistry1111 Expand then factorising LHS gives (a+b)x + (2a + 3b) = 18x + 8 --> by comparing coefficients, you obtain a+b = 18 and 2a+3b =8, solve simultaneously for a and b, giving a=46 and b=-28
chemistry1111 thank you so much that makes sense also this question For the polynomial P(x)=(a+1)x3 + (b-7)x2 +c+5, find values for a,b and c if P(x) has a degree 2, a leading coefficient of 3 and the constant term is -1
chemistry1111 when factorizing polynomials in methods unit 3/4, what method do most people use vcaa prefer, long division or equating coefficients
PizzaMaster Do we need to buy the new Methods 3/4 book for the new study design (2023)? I feel like the textbook questions are the same...
PizzaMaster Can anyone plz help with this question (part b, c and d in particular): https://imgur.com/a/7hzDLFw
jinx_58 PizzaMaster Howdy, I did QCE Methods, so if I mess this up, I’m really sorry. https://ibb.co/m0Q1xdV For b) may I know what the answers are? I may be able to work backwards 🙂 I didn’t do d) because I wasn’t that confident in doing the question. Hope this helps, -jinx_58
PizzaMaster Hi jinx_58, Thank you so much for solving! The answer to part b is Domain = [0, 6]; Range = [0, 9/2] The answer to part c is 9/2
chemistry1111 The graph of y = 5/x -6 is reflected in the x-axis and then in the y-axis. The equation of the final image is: could someone help with this question
crumblycupcakes chemistry1111 reflected in the x-axis reflected in the y-axis **I'm not quite sure if y = (5/x) -6 or if it's y = 5/(x-6) so I'll show the working for both let f[x] = (5/x) -6 x reflection: -f[x] = f1[x] = -[ (5/x) - 6 ] = -( 5/x ) + 6 y reflection: f1[-x] = f2[x] = -(5/ [-x] ) +6 = -(5/ x ) +6 let g[x] = 5/(x-6) x reflection: -g[x] = f1[x] = -[ 5/(x-6) ] = -5/(x-6) y reflection: g1[-x] = f2[x] = -5/( [-x] - 6) = -5/( -x - 6) hope that helps!
