Math Is Fun Forum

dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Algebra help

1) Similarly, by restricting the domain of the function f(x)=2x^2-4x-5 to an interval, we can make it invertible. What is the largest such interval that includes the point x=0?

2)Suppose the domain of f is (-1,1). Define the function h by h(x)=f(x)+1.  What is the domain of h?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Algebra help

hi dazzle1230

Q1.  That's a quadratic.  Sketch the graph and all except the lowest point have two x values for each y.

So to make it invertible you can choose any domain that stops that happening: eg from the lowest point rightwards.

x=0 isn't the lowest point so you should be able to find the required interval to include it and also be the largest.

Q2.  Sketch a random wiggly line for f(x) between x = -1 and +1.

Now sketch h(x) by just moving the wiggly line up by 1.  Looks to me like the domain is the same.

Bob

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dazzle1230

Member

Registered: 2016-05-17

Posts: 92

Re: Algebra help

for Q1, I put in (-inf, 1) but it was wrong

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Algebra help

for Q1, I put in (-inf, 1) but it was wrong

Should it be (-inf, 1] ?I mean closed at 1.

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