Consider the given functions,
Solve for f(2) as,
Thus, the value of f(2) is equal to 1 .
Solve for inverse of f(1) as,
Thus, the value of f(2) is equal to 1 .
I attached the solutions for you, if you have any questions just message me. I will be more than happy to help.
Answer:
whats the info below i cant see it?
Step-by-step explanation:
<span><span><span>Given <span>f(x) = 2x + 3</span><span> and </span><span>g(x) = –x2 + 5</span><span>, find </span></span><span>(<span> f</span> </span>o<span> f )(x</span><span>).</span></span><span>(<span> f</span> </span>o<span> <span>f </span>)(x) = f (<span> f</span> (x))</span><span>
</span><span> = f (2x + 3)</span><span>
</span><span> = 2( ) + 3 </span>... setting up to insert the input<span>
</span><span> = 2(2x + 3) + 3</span><span>
</span><span> = 4x + 6 + 3</span><span>
</span> <span>= 4x + 9</span></span><span><span><span><span>Given </span><span>f(x) = 2x + 3</span><span> and </span><span>g(x) = –x2 + 5</span><span>, find </span></span><span>(g</span><span> o</span><span> g)(x</span><span>).</span></span><span>(g </span>o<span> g)(x) = g(g(x))</span><span>
</span><span> = –( )2 + 5 </span>... setting up to insert the input<span>
</span><span> = –(–x2 + 5)2 + 5</span><span>
</span><span> = –(x4 – 10x2 + 25) + 5</span><span>
</span><span> = –x4 + 10x2 – 25 + 5</span><span>
</span><span> = </span><span>–x4 + 10x2 – 20</span></span>
Sometimes you have to be careful with the domain and range of the composite function.
<span><span><span>Given </span><span>f (x) = sqrt(x)</span><span> and </span><span>g(x) = x – 2</span><span>, find the domains of </span><span>(<span> f</span> </span>o<span> g)(x)</span><span> and </span><span>(g </span>o<span> f )(x)</span>.</span></span>
