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## the function f(x) is defined by f(x)=x^2+3x-10?

f(x) = x^2 + 3x − 10

∴ f(x + 5) = (x + 5)^2 + 3(x + 5) − 10

∴ f(x + 5) = x^2 + 10x + 25 + 3x + 15 − 10

∴ f(x + 5) = x^2 + 13x − 30

given x^2 + 13x − 30 = x^2 + kx + 30

∴ 13x − kx = 60

∴ (13 − k)x = 60

∴ 13 − k = 60/x

∴ 13 − 60/x = k

however is you meant f(x + 5) = x^2 + kx − 30 instead

given x^2 + 13x − 30 = x^2 + kx − 30

∴ 13x = kx

∴ k = 13

now f(x + 5) = x^2 + 13x − 30

∴ f(x + 5) = x^2 + 15x − 2x − 30

∴ f(x + 5) = x(x + 15) − 2(x + 15)

∴ f(x + 5) = (x + 15)(x − 2)

∴ when f(x + 5) = 0 then x + 15 = 0 and x − 2 =0

∴ smallist x = -15

C3 Functions – …function is defined by f ( x) 2cos 1 x 1 . (i) Write down the domain and range of this function. (ii) Find the value of f(-0.5). (iii) Find the inverse function copy; MEI, 10/05/10 2/8 MEI C3 Functions Assessment solutions Functions / Natural logarithms and exponentials Solutions to Chapter…We can construct the new function.Click here to see ALL problems on Rational-functions. Question 170124: Let the function f be defined by f(x)=x+1. You can put this solution on YOUR website! Let the function f be defined by f(x)=x+1.

Discontinuous Functions – Page 2 – Therefore for 0≤x≤10, the images of f(x) are unique Thus the given relation is a function The relation g is defined as g(x)={x2,0≤x≤23x,2≤x≤10 It can be observed that for x=2,g(x)=22=4 and g(x)=3×2=6